--- a/drafts/rdf11-mt/Overview.html Thu Oct 31 14:44:06 2013 -0700
+++ b/drafts/rdf11-mt/Overview.html Fri Nov 01 13:34:00 2013 +0100
@@ -1,11 +1,11 @@
<!DOCTYPE html>
-<html lang="en" dir="ltr" typeof="bibo:Document w3p:LastCall" about="" property="dcterms:language" content="en">
+<html lang="en" dir="ltr" typeof="bibo:Document w3p:CR" about="" property="dcterms:language" content="en">
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- <meta http-equiv="Content-Type" content="text/html;charset=utf-8">
- <title>RDF 1.1 Semantics</title>
+ <meta http-equiv="Content-Type" content="text/html;charset=utf-8">
+ <title>RDF 1.1 Semantics</title>
-
+
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@@ -170,20 +170,20 @@
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margin-bottom: 0;
}
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+ <body id="respecDocument" role="document" class="h-entry"><div id="respecHeader" role="contentinfo" class="head">
<p>
- <a href="http://www.w3.org/"><img src="http://www.w3.org/Icons/w3c_home" alt="W3C" height="48" width="72"></a>
+ <a href="http://www.w3.org/"><img src="https://www.w3.org/Icons/w3c_home" alt="W3C" height="48" width="72"></a>
</p>
<h1 class="title p-name" id="title" property="dcterms:title">RDF 1.1 Semantics</h1>
- <h2 id="w3c-last-call-working-draft-23-july-2013" property="dcterms:issued" datatype="xsd:dateTime" content="2013-07-22T22:00:00.000Z"><abbr title="World Wide Web Consortium">W3C</abbr> Last Call Working Draft <time class="dt-published" datetime="2013-07-23">23 July 2013</time></h2>
+ <h2 id="w3c-candidate-recommendation-05-november-2013" property="dcterms:issued" datatype="xsd:dateTime" content="2013-11-05T08:00:00.000Z"><abbr title="World Wide Web Consortium">W3C</abbr> Candidate Recommendation <time class="dt-published" datetime="2013-11-05">05 November 2013</time></h2>
<dl>
<dt>This version:</dt>
- <dd><a class="u-url" href="http://www.w3.org/TR/2013/WD-rdf11-mt-20130723/">http://www.w3.org/TR/2013/WD-rdf11-mt-20130723/</a></dd>
+ <dd><a class="u-url" href="http://www.w3.org/TR/2013/CR-rdf11-mt-20131105/">http://www.w3.org/TR/2013/CR-rdf11-mt-20131105/</a></dd>
<dt>Latest published version:</dt>
<dd><a href="http://www.w3.org/TR/rdf11-mt/">http://www.w3.org/TR/rdf11-mt/</a></dd>
@@ -192,6 +192,9 @@
<dd><a href="https://dvcs.w3.org/hg/rdf/raw-file/default/rdf-mt/index.html">https://dvcs.w3.org/hg/rdf/raw-file/default/rdf-mt/index.html</a></dd>
+ <dt>Test suite:</dt>
+ <dd><a href="http://www.w3.org/2013/rdf-mt-tests/">http://www.w3.org/2013/rdf-mt-tests/</a></dd>
+
@@ -199,8 +202,10 @@
<dd><a rel="dcterms:replaces" href="http://www.w3.org/TR/2013/WD-rdf11-mt-20130409/">http://www.w3.org/TR/2013/WD-rdf11-mt-20130409/</a></dd>
- <dt>Latest recommendation:</dt>
- <dd><a href="http://www.w3.org/TR/rdf-mt/">http://www.w3.org/TR/rdf-mt/</a></dd>
+
+ <dt>Latest Recommendation:</dt>
+ <dd><a href="http://www.w3.org/TR/rdf-mt/">http://www.w3.org/TR/rdf-mt/</a></dd>
+
<dt>Editors:</dt>
<dd class="p-author h-card vcard" rel="bibo:editor" inlist=""><span typeof="foaf:Person"><a class="u-url url p-name fn" rel="foaf:homepage" property="foaf:name" content="Patrick J. Hayes" href="http://www.ihmc.us/groups/phayes/">Patrick J. Hayes</a>, <a rel="foaf:workplaceHomepage" class="p-org org h-org h-card" href="http://www.ihmc.us/index.php">Florida IHMC</a></span>
@@ -223,19 +228,25 @@
<a href="http://www.w3.org/"><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup>
(<a href="http://www.csail.mit.edu/"><abbr title="Massachusetts Institute of Technology">MIT</abbr></a>,
<a href="http://www.ercim.eu/"><abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>,
- <a href="http://www.keio.ac.jp/">Keio</a>, <a href="http://ev.buaa.edu.cn/">Beihang</a>), All Rights Reserved.
+ <a href="http://www.keio.ac.jp/">Keio</a>, <a href="http://ev.buaa.edu.cn/">Beihang</a>),
+
+ All Rights Reserved.
+
<abbr title="World Wide Web Consortium">W3C</abbr> <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>,
<a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a> and
- <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> rules apply.
+
+ <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a>
+
+ rules apply.
</p>
<hr>
</div>
- <section rel="bibo:chapter" resource="#abstract" typeof="bibo:Chapter" datatype="" property="dcterms:abstract" class="introductory" id="abstract"><h2>Abstract</h2>
- <p> This document describes a precise semantics for the Resource Description
+ <section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" datatype="" property="dcterms:abstract" class="introductory" id="abstract"><h2 id="h2_abstract" role="heading" aria-level="1">Abstract</h2>
+ <p> This document describes a precise semantics for the Resource Description
Framework 1.1 [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>] and RDF Schema [<cite><a href="#bib-RDF-SCHEMA" class="bibref">RDF-SCHEMA</a></cite>]. It defines a number of distinct entailment regimes and corresponding patterns of entailment. It is part of a suite of documents which comprise the full specification of RDF 1.1.</p>
- </section><section rel="bibo:chapter" resource="#sotd" typeof="bibo:Chapter" id="sotd" class="introductory"><h2>Status of This Document</h2>
+ </section><section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" id="sotd" class="introductory"><h2 id="h2_sotd" role="heading" aria-level="1">Status of This Document</h2>
@@ -250,7 +261,7 @@
[<cite><a href="#bib-RDF-MT" class="bibref">RDF-MT</a></cite>] and supersedes that document.</p>
<p>
- This document was published by the <a href="http://www.w3.org/2011/rdf-wg/">RDF Working Group</a> as a Last Call Working Draft.
+ This document was published by the <a href="http://www.w3.org/2011/rdf-wg/">RDF Working Group</a> as a Candidate Recommendation.
This document is intended to become a <abbr title="World Wide Web Consortium">W3C</abbr> Recommendation.
@@ -260,24 +271,24 @@
(<a href="mailto:public-rdf-comments-request@w3.org?subject=subscribe">subscribe</a>,
<a href="http://lists.w3.org/Archives/Public/public-rdf-comments/">archives</a>).
- The Last Call period ends 06 September 2013.
+
+
+ <abbr title="World Wide Web Consortium">W3C</abbr> publishes a Candidate Recommendation to indicate that the document is believed
+ to be stable and to encourage implementation by the developer community. This
+ Candidate Recommendation is expected to advance to Proposed Recommendation no earlier than
+ 26 November 2013.
All comments are welcome.</p>
<p>
- Publication as a Last Call Working Draft does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
+ Publication as a Candidate Recommendation does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
This is a draft document and may be updated, replaced or obsoleted by other documents at
any time. It is inappropriate to cite this document as other than work in progress.
</p>
- <p>
- This is a Last Call Working Draft and thus the Working Group has determined that this document has satisfied the
- relevant technical requirements and is sufficiently stable to advance through the Technical Recommendation process.
- </p>
-
<p>
This document was produced by a group operating under the
@@ -302,20 +313,20 @@
-</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a class="tocxref" href="#introduction-1"><span class="secno">1. </span>Introduction</a></li><li class="tocline"><a class="tocxref" href="#conformance"><span class="secno">2. </span>Conformance</a></li><li class="tocline"><a class="tocxref" href="#semantic-extensions-and-entailment-regimes"><span class="secno">3. </span>Semantic Extensions and Entailment Regimes</a></li><li class="tocline"><a class="tocxref" href="#notation-and-terminology"><span class="secno">4. </span>Notation and Terminology</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#shared-blank-nodes-unions-and-merges"><span class="secno">4.1 </span>Shared blank nodes, unions and merges</a></li></ul></li><li class="tocline"><a class="tocxref" href="#simple-interpretations"><span class="secno">5. </span> Simple Interpretations</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#blank-nodes"><span class="secno">5.1 </span>Blank nodes</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#shared-blank-nodes-informative"><span class="secno">5.1.1 </span>Shared blank nodes (Informative)</a></li></ul></li><li class="tocline"><a class="tocxref" href="#intuitive-summary-informative"><span class="secno">5.2 </span>Intuitive summary (Informative)</a></li><li class="tocline"><a class="tocxref" href="#simpleentailment"><span class="secno">5.3 </span>Simple Entailment</a></li><li class="tocline"><a class="tocxref" href="#properties-of-simple-entailment-informative"><span class="secno">5.4 </span>Properties of simple entailment (Informative) </a></li></ul></li><li class="tocline"><a class="tocxref" href="#skolemization-informative"><span class="secno">6. </span>Skolemization (Informative)</a></li><li class="tocline"><a class="tocxref" href="#literals-and-datatypes"><span class="secno">7. </span>Literals and datatypes</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#D_interpretations"><span class="secno">7.1 </span>D-interpretations</a></li><li class="tocline"><a class="tocxref" href="#datatype-entailment"><span class="secno">7.2 </span>Datatype entailment</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#patterns-of-datatype-entailment-informative"><span class="secno">7.2.1 </span>Patterns of datatype entailment (Informative)</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#rdf-interpretations"><span class="secno">8. </span>RDF Interpretations</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#rdf-entailment"><span class="secno">8.1 </span>RDF entailment</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#patterns-of-rdf-entailment-informative"><span class="secno">8.1.1 </span>Patterns of RDF entailment (Informative)</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#rdfs-interpretations"><span class="secno">9. </span>RDFS Interpretations</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#a-note-on-rdfs-literal-informative"><span class="secno">9.1 </span>A note on rdfs:Literal (Informative)</a></li><li class="tocline"><a class="tocxref" href="#rdfs-entailment"><span class="secno">9.2 </span>RDFS entailment</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#patterns-of-rdfs-entailment-informative"><span class="secno">9.2.1 </span>Patterns of RDFS entailment (Informative)</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#rdf-datasets"><span class="secno">10. </span>RDF Datasets</a></li><li class="tocline"><a class="tocxref" href="#entailment-rules-informative"><span class="secno">A. </span>Entailment rules (Informative)</a></li><li class="tocline"><a class="tocxref" href="#finite-interpretations-informative"><span class="secno">B. </span>Finite interpretations (Informative)</a></li><li class="tocline"><a class="tocxref" href="#proofs-of-some-results-informative"><span class="secno">C. </span>Proofs of some results (Informative)</a></li><li class="tocline"><a class="tocxref" href="#whatnot"><span class="secno">D. </span>RDF reification, containers and collections (Informative)</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#reification"><span class="secno">D.1 </span>Reification</a></li><li class="tocline"><a class="tocxref" href="#rdf-containers"><span class="secno">D.2 </span>RDF containers</a></li><li class="tocline"><a class="tocxref" href="#rdf-collections"><span class="secno">D.3 </span>RDF collections</a></li></ul></li><li class="tocline"><a class="tocxref" href="#acknowledgements-1"><span class="secno">E. </span>Acknowledgements</a></li><li class="tocline"><a class="tocxref" href="#references"><span class="secno">F. </span>References</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#normative-references"><span class="secno">F.1 </span>Normative references</a></li><li class="tocline"><a class="tocxref" href="#informative-references"><span class="secno">F.2 </span>Informative references</a></li></ul></li></ul></section>
+</section><section id="toc"><h2 id="h2_toc" role="heading" aria-level="1" class="introductory">Table of Contents</h2><ul id="respecContents" role="directory" class="toc"><li class="tocline"><a class="tocxref" href="#introduction-1"><span class="secno">1. </span>Introduction</a></li><li class="tocline"><a class="tocxref" href="#conformance"><span class="secno">2. </span>Conformance</a></li><li class="tocline"><a class="tocxref" href="#semantic-extensions-and-entailment-regimes"><span class="secno">3. </span>Semantic Extensions and Entailment Regimes</a></li><li class="tocline"><a class="tocxref" href="#notation-and-terminology"><span class="secno">4. </span>Notation and Terminology</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#shared-blank-nodes-unions-and-merges"><span class="secno">4.1 </span>Shared blank nodes, unions and merges</a></li></ul></li><li class="tocline"><a class="tocxref" href="#simple-interpretations"><span class="secno">5. </span> Simple Interpretations</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#blank-nodes"><span class="secno">5.1 </span>Blank nodes</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#shared-blank-nodes-informative"><span class="secno">5.1.1 </span>Shared blank nodes (Informative)</a></li></ul></li><li class="tocline"><a class="tocxref" href="#simpleentailment"><span class="secno">5.2 </span>Simple Entailment</a></li><li class="tocline"><a class="tocxref" href="#properties-of-simple-entailment-informative"><span class="secno">5.3 </span>Properties of simple entailment (Informative) </a></li></ul></li><li class="tocline"><a class="tocxref" href="#skolemization-informative"><span class="secno">6. </span>Skolemization (Informative)</a></li><li class="tocline"><a class="tocxref" href="#literals-and-datatypes"><span class="secno">7. </span>Literals and datatypes</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#D_interpretations"><span class="secno">7.1 </span>D-interpretations</a></li><li class="tocline"><a class="tocxref" href="#datatype-entailment"><span class="secno">7.2 </span>Datatype entailment</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#patterns-of-datatype-entailment-informative"><span class="secno">7.2.1 </span>Patterns of datatype entailment (Informative)</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#rdf-interpretations"><span class="secno">8. </span>RDF Interpretations</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#rdf-entailment"><span class="secno">8.1 </span>RDF entailment</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#patterns-of-rdf-entailment-informative"><span class="secno">8.1.1 </span>Patterns of RDF entailment (Informative)</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#rdfs-interpretations"><span class="secno">9. </span>RDFS Interpretations</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#a-note-on-rdfs-literal-informative"><span class="secno">9.1 </span>A note on rdfs:Literal (Informative)</a></li><li class="tocline"><a class="tocxref" href="#rdfs-entailment"><span class="secno">9.2 </span>RDFS entailment</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#patterns-of-rdfs-entailment-informative"><span class="secno">9.2.1 </span>Patterns of RDFS entailment (Informative)</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#rdf-datasets"><span class="secno">10. </span>RDF Datasets</a></li><li class="tocline"><a class="tocxref" href="#entailment-rules-informative"><span class="secno">A. </span>Entailment rules (Informative)</a></li><li class="tocline"><a class="tocxref" href="#finite-interpretations-informative"><span class="secno">B. </span>Finite interpretations (Informative)</a></li><li class="tocline"><a class="tocxref" href="#proofs-of-some-results-informative"><span class="secno">C. </span>Proofs of some results (Informative)</a></li><li class="tocline"><a class="tocxref" href="#whatnot"><span class="secno">D. </span>RDF reification, containers and collections (Informative)</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#reification"><span class="secno">D.1 </span>Reification</a></li><li class="tocline"><a class="tocxref" href="#rdf-containers"><span class="secno">D.2 </span>RDF containers</a></li><li class="tocline"><a class="tocxref" href="#rdf-collections"><span class="secno">D.3 </span>RDF collections</a></li></ul></li><li class="tocline"><a class="tocxref" href="#change-log-informative"><span class="secno">E. </span>Change Log (informative)</a></li><li class="tocline"><a class="tocxref" href="#acknowledgements-1"><span class="secno">F. </span>Acknowledgements</a></li><li class="tocline"><a class="tocxref" href="#references"><span class="secno">G. </span>References</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#normative-references"><span class="secno">G.1 </span>Normative references</a></li><li class="tocline"><a class="tocxref" href="#informative-references"><span class="secno">G.2 </span>Informative references</a></li></ul></li></ul></section>
- <section rel="bibo:chapter" resource="#notes" typeof="bibo:Chapter" class="introductory"><h2 id="notes">Notes</h2>
+ <section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="introductory"><h2 role="heading" aria-level="1" id="notes">Notes</h2>
<p class="changenote">Notes in this style indicate changes from the 2004 RDF 1.0 semantics.</p>
<p class="technote">Notes in this style are technical asides on obscure or recondite matters.</p></section>
- <section id="introduction-1" rel="bibo:chapter" resource="#introduction" typeof="bibo:Chapter">
- <!--OddPage--><h2 id="introduction"><span class="secno">1. </span>Introduction</h2>
+ <section id="introduction-1" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
+ <!--OddPage--><h2 role="heading" aria-level="1" id="introduction"><span class="secno">1. </span>Introduction</h2>
<p>
This document defines a model-theoretic semantics for RDF graphs and the RDF and RDFS vocabularies, providing an exact formal specification of when truth is preserved by transformations of RDF or operations which derive RDF content from other RDF. </p>
</section>
-<section rel="bibo:chapter" resource="#conformance" typeof="bibo:Chapter" id="conformance"><!--OddPage--><h2><span class="secno">2. </span>Conformance</h2>
+<section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" id="conformance"><!--OddPage--><h2 id="h2_conformance" role="heading" aria-level="1"><span class="secno">2. </span>Conformance</h2>
<p>
As well as sections marked as non-normative, all authoring guidelines, diagrams, examples,
and notes in this specification are non-normative. Everything else in this specification is
@@ -326,67 +337,70 @@
and <em title="OPTIONAL" class="rfc2119">OPTIONAL</em> in this specification are to be interpreted as described in [<cite><a href="#bib-RFC2119" class="bibref">RFC2119</a></cite>].
</p>
<p>This specification, <em>RDF 1.1 Semantics</em>, is normative for RDF semantics and the validity of RDF inference processes. It is not normative for many aspects of RDF meaning which are not described or specified by this semantics, including social issues of how IRIs are assigned meanings in use and how the referents of IRIs are related to Web content expressed in other media such as natural language texts. </p></section>
-
- <section id="semantic-extensions-and-entailment-regimes" rel="bibo:chapter" resource="#extensions" typeof="bibo:Chapter">
- <!--OddPage--><h2 id="extensions"><span class="secno">3. </span>Semantic Extensions and Entailment Regimes</h2>
+
+ <section id="semantic-extensions-and-entailment-regimes" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
+ <!--OddPage--><h2 role="heading" aria-level="1" id="extensions"><span class="secno">3. </span>Semantic Extensions and Entailment Regimes</h2>
<p>RDF is intended for use as a base notation for a variety of extended notations such as OWL [<cite><a href="#bib-OWL2-OVERVIEW" class="bibref">OWL2-OVERVIEW</a></cite>] and RIF [<cite><a href="#bib-RIF-OVERVIEW" class="bibref">RIF-OVERVIEW</a></cite>], whose expressions can be encoded as RDF graphs which use a particular vocabulary with a specially defined meaning. Also, particular IRI vocabularies may be given meanings by other specifications or conventions. When such extra meanings are assumed, a given RDF graph may support more extensive entailments than are sanctioned by the basic RDF semantics. In general, the more assumptions that are made about the meanings of IRIs in an RDF graph, the more entailments follow from those assumptions. </p>
-<p>A particular such set of semantic assumptions is called a <dfn id="dfn-semantic-extension">semantic extension</dfn>. Each <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a> defines an <dfn id="dfn-entailment-regime">entailment regime</dfn> of entailments which are valid under that extension. RDFS, described later in this document, is one such <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a>. We will refer to an entailment regime by names such as <em> RDFS entailment</em>, <em>D-entailment</em>, etc. </p>
+<p>A particular such set of semantic assumptions is called a <dfn id="dfn-semantic-extension">semantic extension</dfn>. Each <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a> defines an <dfn id="dfn-entailment-regime">entailment regime</dfn> (used here in the same sense as in the SPARQL 1.1 Entailment Regime recommendation [<cite><a href="#bib-SPARQL11-ENTAILMENT" class="bibref">SPARQL11-ENTAILMENT</a></cite>] ) of entailments which are valid under that extension. RDFS, described later in this document, is one such <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a>. We will refer to entailment regimes by names such as <em> RDFS entailment</em>, <em>D-entailment</em>, etc. </p>
<p><a class="internalDFN" href="#dfn-semantic-extension">Semantic extension</a>s <em title="MAY" class="rfc2119">MAY</em> impose special syntactic conditions or restrictions upon RDF graphs, such as requiring certain triples to be present, or prohibiting particular combinations of IRIs in triples, and <em title="MAY" class="rfc2119">MAY</em> consider RDF graphs which do not conform to these conditions to be errors. For example, RDF statements of the form <br><br> <code>ex:a rdfs:subClassOf "Thing"^^xsd:string .</code><br><br> are prohibited in the OWL <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a> based on description logics [<cite><a href="#bib-OWL2-SYNTAX" class="bibref">OWL2-SYNTAX</a></cite>]. In such cases, basic RDF operations such as taking a subset of triples, or combining RDF graphs, may cause syntax errors in parsers which recognize the extension conditions. None of the <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a>s normatively defined in this document impose such syntactic restrictions on RDF graphs.</p>
-<p>All entailment regimes <em title="MUST" class="rfc2119">MUST</em> be <a>monotonic</a> extensions of the simple entailment regime described in the document, in the sense that if A <a class="internalDFN" href="#dfn-simply-entails">simply entails</a> B then A also entails B under any extended notion of entailment, provided that any syntactic conditions of the extension are also satisfied. Put another way, a <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a> cannot "cancel" an entailment made by a weaker entailment regime, although it can treat the result as a syntax error.</p>
+<p>All entailment regimes <em title="MUST" class="rfc2119">MUST</em> be <dfn id="dfn-monotonic">monotonic</dfn> extensions of the simple entailment regime described in the document, in the sense that if A simply <a class="internalDFN" href="#dfn-entail">entail</a>s B then A also entails B under any extended notion of entailment, provided that any syntactic conditions of the extension are also satisfied. Put another way, a <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a> cannot "cancel" an entailment made by a weaker entailment regime, although it can treat the result as a syntax error.</p>
</section>
- <section id="notation-and-terminology" rel="bibo:chapter" resource="#notation" typeof="bibo:Chapter">
- <!--OddPage--><h2 id="notation"><span class="secno">4. </span>Notation and Terminology</h2>
-
-
- <p>This document uses the following terminology for describing RDF graph syntax, all as defined in the companion RDF Concepts specification [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>]: <em><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-iri">IRI</a></em>, <em><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples">RDF triple</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-rdf-graph">RDF graph</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples">subject</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples">predicate</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples">object</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-rdf-source">RDF source</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-node">node</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-blank-node">blank node</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-literal">literal</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#graph-isomorphism">isomorphic</a>, and <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-dataset">RDF datasets</a>.</em> All the definitions in this document apply unchanged to <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-generalized-rdf">generalized RDF triples, graphs, and datasets</a>. </p>
+ <section id="notation-and-terminology" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
+ <!--OddPage--><h2 role="heading" aria-level="1" id="notation"><span class="secno">4. </span>Notation and Terminology</h2>
-<p>The words <dfn id="dfn-denotes">denotes</dfn> and <dfn id="dfn-refers-to">refers to</dfn> are used interchangeably as synonyms for the relationship between an IRI or literal and what it refers to in a given interpretation, itself called the <dfn id="dfn-referent">referent</dfn> or <dfn id="dfn-denotation">denotation</dfn>. IRI meanings may also be determined by other constraints external to the RDF semantics; when we wish to refer to such an externally defined naming relationship, we will use the word <dfn id="dfn-identify">identify</dfn> and its cognates. For example, the fact that the IRI <code>http://www.w3.org/2001/XMLSchema#decimal</code> is widely used as the name of a datatype described in the XML Schema document [<cite><a href="#bib-XMLSCHEMA11-2" class="bibref">XMLSCHEMA11-2</a></cite>] might be described by saying that the IRI <em>identifies</em> that datatype. If an IRI identifies something it may or may not refer to it in a given interpretation, depending on how the semantics is specified. For example, an IRI used as a graph name <a class="internalDFN" href="#dfn-identify">identify</a>ing a named graph in an <a href="http://www.w3.org/TR/rdf11-concepts/#section-dataset" class="external">RDF dataset</a> may refer to something different from the graph it identifies. </p>
+ <p>This document uses the following terminology for describing RDF graph syntax, all as defined in the companion RDF Concepts specification [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>]: <em><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-iri"><dfn id="dfn-iri">IRI</dfn></a></em>, <em><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples"><dfn id="dfn-rdf-triple">RDF triple</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-rdf-graph"><dfn id="dfn-rdf-graph">RDF graph</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples"><dfn id="dfn-subject">subject</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples"><dfn id="dfn-predicate">predicate</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples"><dfn id="dfn-object">object</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-rdf-source"><dfn id="dfn-rdf-source">RDF source</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-node"><dfn id="dfn-node">node</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-blank-node"><dfn id="dfn-blank-node">blank node</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-literal"><dfn id="dfn-literal">literal</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#graph-isomorphism"><dfn id="dfn-isomorphic">isomorphic</dfn></a>, and <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-dataset"><dfn id="dfn-rdf-dataset">RDF dataset</dfn></a>.</em> All the definitions in this document apply unchanged to <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-generalized-rdf">generalized RDF triples, graphs, and datasets</a>. </p>
-<p>Throughout this document, the equality sign = indicates strict identity. The statement "A = B" means that there is one entity to which both expressions "A" and "B" refer. Angle brackets < x, y > are used to indicate an ordered pair
+<p>
+An <dfn id="dfn-interpretation">interpretation</dfn> is a mapping from IRIs and literals into a set, together with some constraints upon the set and the mapping. This document defines various notions of interpretation, each corresponding in a standard way to an entailment regime. These are identified by prefixes such as <em>simple interpretation</em>, etc., and are defined in later sections. The unqualified term <em>interpretation</em> is usually used to refer to any compatible kind of interpretation in general, but if clear from the context might refer to a specific kind of interpretation.
+</p><p>
+
+</p><p>The words <dfn id="dfn-denote">denote</dfn><strong>s</strong> and <dfn id="dfn-refers-to">refers to</dfn> are used interchangeably as synonyms for the relationship between an IRI or literal and what it refers to in a given interpretation, itself called the <dfn id="dfn-denotation">denotation</dfn> or <dfn id="dfn-referent">referent</dfn>. IRI meanings may also be determined by other constraints external to the RDF semantics; when we wish to refer to such an externally defined naming relationship, we will use the word <dfn id="dfn-identify">identify</dfn> and its cognates. For example, the fact that the IRI <code>http://www.w3.org/2001/XMLSchema#decimal</code> is widely used as the name of a datatype described in the XML Schema document [<cite><a href="#bib-XMLSCHEMA11-2" class="bibref">XMLSCHEMA11-2</a></cite>] might be described by saying that the IRI <em>identifies</em> that datatype. If an IRI identifies something it may or may not refer to it in a given interpretation, depending on how the semantics is specified. For example, an IRI used as a graph name <a class="internalDFN" href="#dfn-identify">identify</a>ing a named graph in an <a href="http://www.w3.org/TR/rdf11-concepts/#section-dataset" class="external">RDF dataset</a> may refer to something different from the graph it identifies. </p>
+
+<p>Throughout this document, the equality sign = indicates strict identity. The statement "A = B" means that there is one entity to which both expressions "A" and "B" refer. Angle brackets < x, y > are used to indicate an ordered pair
of x and y.</p>
-<p>Throughout this document, RDF graphs and other fragments of RDF abstract syntax are written using the notational conventions of the Turtle syntax [<cite><a href="#bib-TURTLE-CR" class="bibref">TURTLE-CR</a></cite>]. The namespace prefixes <code>rdf:</code> <code>rdfs:</code> and <code>xsd:</code> are used as in [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>], <a href="http://www.w3.org/TR/rdf11-concepts/#vocabularies">section 1.4</a>. When the exact IRI does not matter, the prefix <code>ex:</code> is used. When stating general rules or conditions we use three-character variables such as aaa, xxx, sss to indicate arbitrary IRIs, literals, or other components of RDF syntax. Some cases are illustrated by node-arc diagrams showing the graph structure directly.</p>
+<p>Throughout this document, <a class="internalDFN" href="#dfn-rdf-graph">RDF graph</a>s and other fragments of RDF abstract syntax are written using the notational conventions of the Turtle syntax [<cite><a href="#bib-TURTLE" class="bibref">TURTLE</a></cite>]. The namespace prefixes <code>rdf:</code> <code>rdfs:</code> and <code>xsd:</code> are used as in [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>], <a href="http://www.w3.org/TR/rdf11-concepts/#vocabularies">section 1.4</a>. When the exact IRI does not matter, the prefix <code>ex:</code> is used. When stating general rules or conditions we use three-character variables such as aaa, xxx, sss to indicate arbitrary IRIs, literals, or other components of RDF syntax. Some cases are illustrated by node-arc diagrams showing the graph structure directly.</p>
<p>A <dfn id="dfn-name">name</dfn> is any IRI or literal. A typed literal contains
- two <a class="internalDFN" href="#dfn-name">name</a>s: itself and its internal type
- IRI. A <dfn id="dfn-vocabulary">vocabulary</dfn> is a set of <a class="internalDFN" href="#dfn-name">name</a>s.
+ two <a class="internalDFN" href="#dfn-name">name</a>s: itself and its internal type
+ IRI. A <dfn id="dfn-vocabulary">vocabulary</dfn> is a set of <a class="internalDFN" href="#dfn-name">name</a>s.
</p>
<p>The <dfn id="dfn-empty-graph">empty graph</dfn> is the empty set of triples. </p>
-<p>A <dfn id="dfn-subgraph">subgraph</dfn> of an RDF graph is a subset
- of the triples in the graph. A triple is identified with the singleton set
- containing it, so that each triple in a graph is considered to be a subgraph.
+<p>A <dfn id="dfn-subgraph">subgraph</dfn> of an RDF graph is a subset
+ of the triples in the graph. A triple is identified with the singleton set
+ containing it, so that each triple in a graph is considered to be a subgraph.
A <dfn id="dfn-proper-subgraph">proper subgraph</dfn> is a proper subset of the triples in the graph. </p>
-
-<p>A <dfn id="dfn-ground">ground</dfn> RDF graph is one that contains no blank
+
+<p>A <dfn id="dfn-ground">ground</dfn> RDF graph is one that contains no blank
nodes.</p>
-<p>Suppose that M is a functional mapping from a set of blank
- nodes to some set of literals, blank nodes and IRIs. Any graph obtained
- from a graph G by replacing some or all of the blank nodes N in G by M(N) is
- an <dfn id="dfn-instance">instance</dfn> of G. Any graph is an instance of itself,
+<p>Suppose that M is a functional mapping from a set of blank
+ nodes to some set of literals, blank nodes and IRIs. Any graph obtained
+ from a graph G by replacing some or all of the blank nodes N in G by M(N) is
+ an <dfn id="dfn-instance">instance</dfn> of G. Any graph is an instance of itself,
an instance of an instance of G is an instance of G,
- and if H is an instance of G then every triple in H is an instance of at least one triple
+ and if H is an instance of G then every triple in H is an instance of at least one triple
in G.</p>
-<p>An <dfn id="dfn-instance-with-respect-to">instance with respect to</dfn> a vocabulary
- V is an <a class="internalDFN" href="#dfn-instance">instance</a> in which all the
- <a class="internalDFN" href="#dfn-name">name</a>s in the instance that were substituted
- for blank nodes in the original are <a class="internalDFN" href="#dfn-name">name</a>s
+<p>An <dfn id="dfn-instance-with-respect-to">instance with respect to</dfn> a vocabulary
+ V is an <a class="internalDFN" href="#dfn-instance">instance</a> in which all the
+ <a class="internalDFN" href="#dfn-name">name</a>s in the instance that were substituted
+ for blank nodes in the original are <a class="internalDFN" href="#dfn-name">name</a>s
from V.</p>
-<p>A <dfn id="dfn-proper-instance">proper instance</dfn> of a graph
- is an <a class="internalDFN" href="#dfn-instance">instance</a> in which a blank node has been replaced by a <a class="internalDFN" href="#dfn-name">name</a>, or two blank
+<p>A <dfn id="dfn-proper-instance">proper instance</dfn> of a graph
+ is an <a class="internalDFN" href="#dfn-instance">instance</a> in which a blank node has been replaced by a <a class="internalDFN" href="#dfn-name">name</a>, or two blank
nodes in the graph have been mapped into the same node in the instance. </p>
-<p>Two graphs are <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#graph-isomorphism">isomorphic</a> when each maps into the other by a 1:1 mapping on blank nodes. Isomorphic graphs are mutual instances with an invertible instance
+<p>Two graphs are <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#graph-isomorphism">isomorphic</a> when each maps into the other by a 1:1 mapping on blank nodes. Isomorphic graphs are mutual instances with an invertible instance
mapping. As blank nodes have no particular identity beyond their location in a graph, we will often treat isomorphic graphs as identical.</p>
-<p>An RDF graph is <dfn id="dfn-lean">lean</dfn> if it has no instance which is
- a proper subgraph of itself. Non-lean graphs have internal redundancy
+<p>An RDF graph is <dfn id="dfn-lean">lean</dfn> if it has no instance which is
+ a proper subgraph of itself. Non-lean graphs have internal redundancy
and express the same content as their lean subgraphs. For example, the graph</p>
<p><code>ex:a ex:p _:x .<br>
_:y ex:p _:x .</code></p>
@@ -396,7 +410,7 @@
<p>is lean. <a class="internalDFN" href="#dfn-ground">Ground</a> graphs are lean. </p>
-<section id="shared-blank-nodes-unions-and-merges" rel="bibo:chapter" resource="#unions_merges" typeof="bibo:Chapter"> <h3 id="unions_merges"><span class="secno">4.1 </span>Shared blank nodes, unions and merges</h3>
+<section id="shared-blank-nodes-unions-and-merges" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter"> <h3 role="heading" aria-level="2" id="unions_merges"><span class="secno">4.1 </span>Shared blank nodes, unions and merges</h3>
<p>
Graphs share blank nodes only if they are derived from graphs
described by documents or other structures (such as an RDF dataset) that explicitly provide for the sharing of blank nodes between different RDF graphs. Simply downloading a
@@ -405,7 +419,7 @@
the same document or from the same <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-rdf-source">RDF source</a>.</p>
<p> RDF applications which manipulate concrete syntaxes for RDF which use blank node identifiers should take care to keep track of the identity of the blank nodes they identify. Blank node identifiers often have a local scope, so when RDF from different sources is combined, identifiers may have to be changed in order to avoid accidental conflation of distinct blank nodes.</p>
-<p> For example, two documents may both use the blank node identifier "<code>_:x</code>" to identify a blank node, but unless these documents are in a shared identifier scope or are derived from a common source, the occurrences of "<code>_:x</code>" in one document will identify a different blank node than the one in the graph described by the other document. When graphs are formed by combining RDF from multiple sources, it may be necessary to <dfn id="dfn-standardize">standardize</dfn> apart the blank node identifiers by replacing them by others which do not occur in the other document(s). For example, the two graphs represented by the following texts: </p>
+<p> For example, two documents may both use the blank node identifier "<code>_:x</code>" to identify a blank node, but unless these documents are in a shared identifier scope or are derived from a common source, the occurrences of "<code>_:x</code>" in one document will identify a different blank node than the one in the graph described by the other document. When graphs are formed by combining RDF from multiple sources, it may be necessary to <dfn id="dfn-standardize">standardize</dfn> apart the blank node identifiers by replacing them by others which do not occur in the other document(s). For example, the two graphs represented by the following texts: </p>
<p><code>ex:a ex:p _:x . </code><br><br>
<img src="RDF11SemanticsDiagrams/example1.jpg" alt="Graph 1"></p>
<p><code>ex:b ex:q _:x . </code><br><br>
@@ -429,7 +443,7 @@
<p>in which the blank node identifiers have been <a class="internalDFN" href="#dfn-standardize">standardize</a>d apart to avoid conflating the distinct blank nodes. (The particular blank node identifiers used have no significance, only that they are distinct.) </p>
<p>It is possible for two or more graphs to share a blank node, for example if they are subgraphs of a single larger graph or derived from a common source. In this case, the union of a set of graphs preserves the identity of blank nodes shared between the graphs. In general, the union of a set of RDF graphs accurately represents the same semantic content as the graphs themselves, whether or not they share blank nodes. </p>
-<p>A related operation, called <dfn id="dfn-merging">merging</dfn>, takes the union after forcing any shared blank nodes, which occur in more than one graph, to be distinct in each graph. The resulting graph is called the <dfn id="dfn-merge">merge</dfn>. The merge of subgraphs of a graph may be larger than the original graph. For example, the result of merging the two singleton subgraphs of the three-node graph</p>
+<p>A related operation, called <dfn id="dfn-merging">merging</dfn>, takes the union after forcing any shared blank nodes, which occur in more than one graph, to be distinct in each graph. The resulting graph is called the <dfn id="dfn-merge">merge</dfn>. The merge of subgraphs of a graph may be larger than the original graph. For example, the result of merging the two singleton subgraphs of the three-node graph</p>
<p><img src="RDF11SemanticsDiagrams/example3.jpg" alt="Three-node Graph"></p>
@@ -444,14 +458,14 @@
</section>
- <section id="simple-interpretations" rel="bibo:chapter" resource="#simple" typeof="bibo:Chapter">
- <!--OddPage--><h2 id="simple"><span class="secno">5. </span> Simple Interpretations</h2>
-
-<p>This section defines the basic notions of interpretation and truth for RDF graphs. All <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a>s of any vocabulary or higher-level notation encoded in RDF <em title="MUST" class="rfc2119">MUST</em> conform to these minimal truth conditions. Other <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a>s may extend and add to these, but they <em title="MUST NOT" class="rfc2119">MUST NOT</em> modify or negate them. For example, because interpretations are mappings which apply to IRIs, a <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a> cannot interpret different occurrences of a single IRI differently.</p>
+ <section id="simple-interpretations" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
+ <!--OddPage--><h2 role="heading" aria-level="1" id="simple"><span class="secno">5. </span> Simple Interpretations</h2>
-<p>The entire semantics applies to <a>RDF graph</a>s, not to <a>RDF source</a>s. An <a>RDF source</a> has a semantic meaning only through the graph that is its value at a given time, or in a given state. Graphs cannot change their semantics with time.</p>
+<p>This section defines the basic notions of simple interpretation and truth for RDF graphs. All <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a>s of any vocabulary or higher-level notation encoded in RDF <em title="MUST" class="rfc2119">MUST</em> conform to these minimal truth conditions. Other <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a>s may extend and add to these, but they <em title="MUST NOT" class="rfc2119">MUST NOT</em> modify or negate them. For example, because simple interpretations are mappings which apply to IRIs, a <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a> cannot interpret different occurrences of a single IRI differently.</p>
-
+<p>The entire semantics applies to <a class="internalDFN" href="#dfn-rdf-graph">RDF graph</a>s, not to <a class="internalDFN" href="#dfn-rdf-source">RDF source</a>s. An <a class="internalDFN" href="#dfn-rdf-source">RDF source</a> has a semantic meaning only through the graph that is its value at a given time, or in a given state. Graphs cannot change their semantics with time.</p>
+
+
<p>A <dfn id="dfn-simple-interpretation">simple interpretation</dfn> I is a structure consisting of:</p>
<div class="tabletitle">Definition of a simple interpretation.</div>
@@ -468,9 +482,9 @@
</tr>
</tbody></table>
-<p class="changenote">The 2004 RDF 1.0 semantics defined interpretations relative to a vocabulary.<br><br>In the 2004 RDF 1.0 semantics, IL was a total, rather than partial, mapping.<br><br> The 2004 RDF 1.0 specification divided literals into 'plain' literals with no type and optional language tags, and typed literals. Usage has shown that it is important that every literal have a type. RDF 1.1 replaces plain literals without language tags by literals typed with the XML Schema <code>string</code> datatype, and introduces the special type <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> for language-tagged strings. The full semantics for typed literals is given in the next section. </p>
+<p class="changenote">The 2004 RDF 1.0 semantics defined simple interpretations relative to a vocabulary.<br><br>In the 2004 RDF 1.0 semantics, IL was a total, rather than partial, mapping.<br><br> The 2004 RDF 1.0 specification divided literals into 'plain' literals with no type and optional language tags, and typed literals. Usage has shown that it is important that every literal have a type. RDF 1.1 replaces plain literals without language tags by literals typed with the XML Schema <code>string</code> datatype, and introduces the special type <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> for language-tagged strings. The full semantics for typed literals is given in the next section. </p>
-<p class="technote"> Interpretations are required to interpret all <a class="internalDFN" href="#dfn-name">name</a>s, and are therefore infinite. This simplifies the exposition. However, RDF can be interpreted using finite structures, supporting decidable algorithms. Details are given in Appendix B. </p>
+<p class="technote"> Simple interpretations are required to interpret all <a class="internalDFN" href="#dfn-name">name</a>s, and are therefore infinite. This simplifies the exposition. However, RDF can be interpreted using finite structures, supporting decidable algorithms. Details are given in Appendix B. </p>
<p>IEXT(x), called
@@ -480,13 +494,13 @@
</p>
<p>The distinction between IR and IL will become significant below when the semantics of datatypes are defined. IL is allowed to be partial because some literals may fail to have a referent. </p>
-<p class="technote">
+<p class="technote">
It is conventional to map a relation name to a relational extension directly. This however presumes that the vocabulary is segregated into relation names and individual names, and RDF makes no such assumption. Moreover, RDF allows an IRI to be used as a relation name applied to itself as an argument. Such self-application structures are used in RDFS, for example. The use of the IEXT mapping to distinguish the relation as an object from its relational extension accommodates both of these requirements. It also provides for a notion of RDFS 'class' which can be distinguished from its set-theoretic extension. A similar technique is used in the ISO/IEC Common Logic standard [<cite><a href="#bib-ISO24707" class="bibref">ISO24707</a></cite>].
</p>
- <p>The denotation of a ground RDF graph in an interpretation I is then given by the following
+ <p>The denotation of a ground RDF graph in a simple interpretation I is then given by the following
rules, where the interpretation is also treated as a function from expressions (names, triples and graphs) to elements of the universe and truth values:</p>
@@ -495,7 +509,7 @@
<tbody>
- <tr>
+ <tr>
<td class="semantictable">if E is a literal then I(E) = IL(E)</td>
</tr>
@@ -504,9 +518,9 @@
</tr>
<tr>
- <td class="semantictable"><p>if E is a ground triple s p o<code>.</code>
+ <td class="semantictable"><p>if E is a ground triple s p o<code>.</code>
then I(E) = true if </p>
- <p>I(p) is in IP and the pair <I(s),I(o)>
+ <p>I(p) is in IP and the pair <I(s),I(o)>
is in IEXT(I(p))</p>
<p>otherwise I(E) = false.</p></td>
</tr>
@@ -523,21 +537,21 @@
<p> The final condition implies that the empty graph (the empty set of triples) is always true.</p>
<p>The sets IP and IR may overlap, indeed IP can be a subset of IR. Because of the domain conditions on IEXT, the denotation of the subject and object of any true triple will be in IR; so any IRI which occurs in a graph both as a predicate and as a subject or object will denote something in the intersection of IP and IR.</p>
-<p><a class="internalDFN" href="#dfn-semantic-extension">Semantic extension</a>s may impose further constraints upon interpretation mappings by requiring some IRIs to refer in particular ways. For example, D-interpretations, described below, require some IRIs, understood as <a class="internalDFN" href="#dfn-identify">identify</a>ing and referring to datatypes, to have a fixed interpretation. </p>
+<p><a class="internalDFN" href="#dfn-semantic-extension">Semantic extension</a>s may impose further constraints upon interpretation mappings by requiring some IRIs to refer in particular ways. For example, D-interpretations, described below, require some IRIs, understood as <a class="internalDFN" href="#dfn-identify">identify</a>ing and referring to datatypes, to have a fixed denotation. </p>
-<section id="blank-nodes" rel="bibo:chapter" resource="#blank_nodes" typeof="bibo:Chapter">
- <h3 id="blank_nodes"><span class="secno">5.1 </span>Blank nodes</h3>
+<section id="blank-nodes" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
+ <h3 role="heading" aria-level="2" id="blank_nodes"><span class="secno">5.1 </span>Blank nodes</h3>
-
-<p>Blank nodes are treated as simply indicating the existence of a thing, without using an IRI to <a class="internalDFN" href="#dfn-identify">identify</a> any particular thing. This is not the same as assuming that the blank node indicates an 'unknown' IRI.
+
+<p>Blank nodes are treated as simply indicating the existence of a thing, without using an IRI to <a class="internalDFN" href="#dfn-identify">identify</a> any particular thing. This is not the same as assuming that the blank node indicates an 'unknown' IRI.
</p>
-<p> Suppose I is an interpretation and A is a mapping from a set of blank nodes to the universe IR of I. Define the mapping [I+A] to be I on <a class="internalDFN" href="#dfn-name">name</a>s, and A on blank nodes on the set: [I+A](x)=I(x) when x is a <a class="internalDFN" href="#dfn-name">name</a> and [I+A](x)=A(x) when x is a blank node; and extend this mapping to triples and RDF graphs using the rules given above for ground graphs. Then the semantic conditions for an RDF graph are:</p>
+<p> Suppose I is a simple interpretation and A is a mapping from a set of blank nodes to the universe IR of I. Define the mapping [I+A] to be I on <a class="internalDFN" href="#dfn-name">name</a>s, and A on blank nodes on the set: [I+A](x)=I(x) when x is a <a class="internalDFN" href="#dfn-name">name</a> and [I+A](x)=A(x) when x is a blank node; and extend this mapping to triples and RDF graphs using the rules given above for ground graphs. Then the semantic conditions for an RDF graph are:</p>
<div class="tabletitle">Semantic condition for blank nodes.</div>
<table border="1">
<tbody>
-
+
<tr>
<td class="semantictable">If E is an RDF graph then I(E) = true if [I+A](E) =
@@ -547,43 +561,46 @@
</tbody>
</table>
-<p>Mappings from blank nodes to referents are not part of the definition of an interpretation, since the truth condition refers only to <em>some</em> such mapping.
+<p>Mappings from blank nodes to referents are not part of the definition of a simple interpretation, since the truth condition refers only to <em>some</em> such mapping.
Blank nodes themselves differ from other nodes in not being assigned
-a denotation by an interpretation, reflecting the intuition that
+a denotation by a simple interpretation, reflecting the intuition that
they have no 'global' meaning. </p>
-<section id="shared-blank-nodes-informative" rel="bibo:chapter" resource="#shared_blank_nodes" typeof="bibo:Chapter" class="informative"><h4 id="shared_blank_nodes"><span class="secno">5.1.1 </span>Shared blank nodes (Informative)</h4><p><em>This section is non-normative.</em></p>
+<section id="shared-blank-nodes-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative"><h4 role="heading" aria-level="3" id="shared_blank_nodes"><span class="secno">5.1.1 </span>Shared blank nodes (Informative)</h4><p><em>This section is non-normative.</em></p>
<p> The semantics for blank nodes are stated in terms of the truth of a graph. However, when two (or more) graphs share a blank node, their meaning is not fully captured by treating them in isolation. For example, consider the overlapping graphs</p>
<p><img src="RDF11SemanticsDiagrams/example5.jpg" alt="Overlapping Graphs"></p>
-<p> and an interpretation I over the universe {Alice, Bob, Monica, Ruth} with:<br>
+<p> and a simple interpretation I over the universe {Alice, Bob, Monica, Ruth} with:<br>
I(<code>ex:Alice</code>)=Alice, I(<code>ex:Bob</code>)=Bob, IEXT(I(<code>ex:hasChild</code>))={<Alice,Monica>,<Bob,Ruth> }<br></p>
<p>Each of the inner graphs is true under this interpretation, but the two of them together is not, because the three-node graph says that Alice and Bob have a child together. In order to capture the full meaning of graphs sharing a blank node, it is necessary to consider the union graph containing all the triples which contain the blank node.</p>
-<p class="technote"> RDF graphs can be viewed as conjunctions of simple atomic sentences in first-order logic, where blank nodes are free variables which are understood to be existential. Taking the union of two graphs is then analogous to syntactic conjunction in this syntax. RDF syntax has no explicit variable-binding quantifiers, so the truth conditions for any RDF graph treat the free variables in that graph as existentially quantified in that graph. Taking the union of graphs which share a blank node changes the implied quantifier scopes.
+<p class="technote"> RDF graphs can be viewed as conjunctions of simple atomic sentences in first-order logic, where blank nodes are free variables which are understood to be existential. Taking the union of two graphs is then analogous to syntactic conjunction in this syntax. RDF syntax has no explicit variable-binding quantifiers, so the truth conditions for any RDF graph treat the free variables in that graph as existentially quantified in that graph. Taking the union of graphs which share a blank node changes the implied quantifier scopes.
</p>
</section>
</section>
-<section id="intuitive-summary-informative" rel="bibo:chapter" resource="#intuitions" typeof="bibo:Chapter" class="informative">
-<h3 id="intuitions" class="informative"><span class="secno">5.2 </span>Intuitive summary (Informative)</h3><p><em>This section is non-normative.</em></p>
+
+<!-- commented out, to be removed later
+<section class="informative">
+<h3 id="intuitions" class="informative">Intuitive summary (Informative)</h3>
<p>An RDF graph is true exactly when:</p>
<p>1. the IRIs and literals in subject or object position in the graph all refer to things,</p><p>2. there is some way to interpret all the blank nodes in the graph as referring to things,</p><p>3. the IRIs in property position refer to binary relationships,</p><p>4. and under these interpretations, each triple S P O in the graph asserts that the thing referred to as S, and the thing referred to as O, do in fact stand in the relationship referred to by P. </p>
-
-</section>
-<section rel="bibo:chapter" resource="#simpleentailment" typeof="bibo:Chapter" id="simpleentailment"><h3><span class="secno">5.3 </span>Simple Entailment</h3>
+</section>
+-->
-<p>Following standard terminology, we say that I <dfn id="dfn-satisfies">satisfies</dfn> E when I(E)=true, that E is <dfn id="dfn-satisfiable">satisfiable</dfn> when an interpretation exists which satisfies it, (otherwise <dfn id="dfn-unsatisfiable">unsatisfiable</dfn>), and that a graph G <dfn id="dfn-simply-entails">simply entails</dfn> a graph E when every interpretation which satisfies G also satisfies E. </p>
+<section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" id="simpleentailment"><h3 id="h3_simpleentailment" role="heading" aria-level="2"><span class="secno">5.2 </span>Simple Entailment</h3>
+
+<p>Following standard terminology, we say that I (simply) <dfn id="dfn-satisfies">satisfies</dfn> E when I(E)=true, that E is (simply) <dfn id="dfn-satisfiable">satisfiable</dfn> when a simple interpretation exists which satisfies it, otherwise (simply) <dfn id="dfn-unsatisfiable">unsatisfiable</dfn>, and that a graph G simply <dfn id="dfn-entail">entail</dfn><strong>s</strong> a graph E when every interpretation which satisfies G also satisfies E. If two graphs E and F each entail the other then they are logically <dfn id="dfn-equivalent">equivalent</dfn>.</p>
<p>In later sections these notions will be adapted to other classes of interpretations, but throughout this section 'entailment' should be interpreted as meaning simple entailment.
</p>
<p class="technote">We do not define a notion of entailment between sets of graphs. To determine whether a set of graphs entails a graph, the graphs in the set must first be combined into one graph, either by taking the union or the merge of the graphs. Unions preserve the common meaning of shared blank nodes, while merging effectively ignores any sharing of blank nodes. Merging the set of graphs produces the same definition of entailment by a set that was defined in the 2004 RDF 1.0 specification.</p>
- <p><a id="defvalid">Any process which constructs a graph E from
+ <p>Any process which constructs a graph E from
some other graph S is (simply) <dfn id="dfn-valid">valid</dfn> if S
- simply entails E in every case, otherwise <dfn id="dfn-invalid.">invalid.</dfn></a></p>
+ simply entails E in every case, otherwise <dfn id="dfn-invalid.x">invalid.</dfn></p>
<p>The fact that an inference is valid should not be understood as meaning that any RDF application is obliged or required to make the inference. Similarly, the logical invalidity of some RDF transformation or process does not mean that the process is incorrect or prohibited. Nothing in this specification requires or prohibits any particular operations on RDF graphs or sources. Entailment and validity are concerned solely with establishing the conditions on such operations which guarantee the preservation of truth. While logically invalid processes, which do not follow valid entailments, are not prohibited, users should be aware that they may be at risk of introducing falsehoods into true RDF data. Nevertheless, particular uses of logically invalid processes may be justified and appropriate for data processing under circumstances where truth can be ensured by other means. </p>
@@ -591,93 +608,93 @@
</section>
-<section id="properties-of-simple-entailment-informative" rel="bibo:chapter" resource="#simple_entailment_properties" typeof="bibo:Chapter" class="informative">
+<section id="properties-of-simple-entailment-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative">
-<h3 id="simple_entailment_properties"><span class="secno">5.4 </span>Properties of simple entailment (Informative) </h3><p><em>This section is non-normative.</em></p>
+<h3 role="heading" aria-level="2" id="simple_entailment_properties"><span class="secno">5.3 </span>Properties of simple entailment (Informative) </h3><p><em>This section is non-normative.</em></p>
<p>The properties described here apply only to simple entailment, not to extended notions of entailment introduced in later sections. Proofs are given in Appendix C. </p>
-<p class="fact">Every graph is satisfiable.</p>
+<p class="fact">Every graph is simply satisfiable.</p>
-<p>This does not hold for extended notions of interpretation. For example, a graph containing an <a class="internalDFN" href="#dfn-ill-typed">ill-typed</a> literal is <a class="internalDFN" href="#dfn-d-unsatisfiable">D-unsatisfiable</a>.</p>
+<p>This does not always hold for extended notions of interpretation. For example, a graph containing an <a class="internalDFN" href="#dfn-ill-typed">ill-typed</a> literal is <a class="internalDFN" href="#dfn-d-unsatisfiable">D-unsatisfiable</a>.</p>
<p>The following <dfn id="dfn-interpolation">interpolation</dfn> <strong>lemma</strong> </p>
<p class="fact">
- G simply entails a graph E if and only if a subgraph of G is an instance of E.
+ G simply entails a graph E if and only if a subgraph of G is an instance of E.
</p>
-<p> completely characterizes simple entailment in syntactic
- terms. To detect whether one RDF graph simply entails another, check that
+<p> completely characterizes simple entailment in syntactic
+ terms. To detect whether one RDF graph simply entails another, check that
there is some instance of the entailed graph which is a subset of the first graph. </p>
-<p class="technote">This is clearly decidable, but it is also difficult to determine in general, since one can encode the NP-hard subgraph problem (detecting whether one mathematical graph is a subgraph of another) as detecting simple entailment between RDF graphs. This construction (due to Jeremy Carroll) uses graphs containing many blank nodes, which are unlikely to occur in practice. The complexity of checking simple entailment is reduced by having fewer blank nodes in the conclusion E. When E is a <a class="internalDFN" href="#dfn-ground">ground</a> graph, it is simply a matter of checking the subset relationship on sets of triples.</p>
+<p class="technote">This is clearly decidable, but it is also difficult to determine in general, since one can encode the NP-hard subgraph problem (detecting whether one mathematical graph is a subgraph of another) as detecting simple entailment between RDF graphs. This construction (due to Jeremy Carroll) uses graphs all of whose nodes are blank nodes. The complexity of checking simple entailment is reduced by having fewer blank nodes in the conclusion E. When E is a <a class="internalDFN" href="#dfn-ground">ground</a> graph, it is simply a matter of checking the subset relationship on sets of triples.</p>
<p><a class="internalDFN" href="#dfn-interpolation">Interpolation</a> has a number of direct consequences, for example:</p>
-<p class="fact"> The <a class="internalDFN" href="#dfn-empty-graph">empty graph</a> is entailed by
- any graph, and does not entail any graph except itself.
+<p class="fact"> The <a class="internalDFN" href="#dfn-empty-graph">empty graph</a> is simply entailed by
+ any graph, and does not simply entail any graph except itself.
<!-- <a href="#emptygraphlemmaprf" class="termref">[Proof]</a> -->
</p>
-<p class="fact"> A graph entails all its subgraphs.
+<p class="fact"> A graph simply entails all its subgraphs.
<!-- <a href="#subglemprf" class="termref">[Proof]</a> -->
</p>
-<p class="fact"> A graph
- is entailed by any of its <a class="internalDFN" href="#dfn-instance">instance</a>s.
+<p class="fact"> A graph
+ is simply entailed by any of its <a class="internalDFN" href="#dfn-instance">instance</a>s.
<!-- <a href="#instlemprf" class="termref"> [Proof]</a> -->
</p>
-<p class="fact"> If
- E is a <a class="internalDFN" href="#dfn-lean">lean</a> graph and E' is a <a class="internalDFN" href="#dfn-proper-instance">proper instance</a> of E, then E does
- not entail E'.
+<p class="fact"> If
+ E is a <a class="internalDFN" href="#dfn-lean">lean</a> graph and E' is a <a class="internalDFN" href="#dfn-proper-instance">proper instance</a> of E, then E does
+ not simply entail E'.
</p>
-
-<p class="fact"> If S is a subgraph of S' and S entails E, then S' entails E.
+
+<p class="fact"> If S is a subgraph of S' and S simply entails E, then S' simply entails E.
<!-- <a href="#monotonicitylemmaprf" class="termref"> [Proof]</a> -->
</p>
-<p class="fact">
- If S entails a finite graph E, then some finite subset S' of S entails E.
+<p class="fact">
+ If S entails a finite graph E, then some finite subset S' of S entails E.
<!-- <a href="#compactlemmaprf" class="termref"> [Proof]</a> -->
</p>
<p>The property just above is called <em>compactness</em> - RDF is compact. As RDF graphs can be infinite, this is sometimes important.</p>
-<p class="fact"> If E contains an IRI which does not occur anywhere in S, then S does not entail E.</p>
+<p class="fact"> If E contains an IRI which does not occur anywhere in S, then S does not simply entail E.</p>
</section>
</section>
-<section id="skolemization-informative" rel="bibo:chapter" resource="#skolemization" typeof="bibo:Chapter" class="informative"><!--OddPage--><h2 id="skolemization"><span class="secno">6. </span>Skolemization (Informative)</h2><p><em>This section is non-normative.</em></p>
-<p><a class="externaldefinition">Skolemization</a> is a transformation on RDF graphs which eliminates blank nodes by replacing them with "new" IRIs, which means IRIs which are coined for this purpose and are therefore guaranteed to not occur in any other RDF graph (at the time of creation). See <a href="http://www.w3.org/TR/rdf11-concepts/#section-skolemization">Section 3.5</a> of [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>] for a fuller discussion. </p>
+<section id="skolemization-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative"><!--OddPage--><h2 role="heading" aria-level="1" id="skolemization"><span class="secno">6. </span>Skolemization (Informative)</h2><p><em>This section is non-normative.</em></p>
+<p><a href="#dfn-skolemization" class="externaldefinition internalDFN"><dfn id="dfn-skolemization">Skolemization</dfn></a> is a transformation on RDF graphs which eliminates blank nodes by replacing them with "new" IRIs, which means IRIs which are coined for this purpose and are therefore guaranteed to not occur in any other RDF graph (at the time of creation). See <a href="http://www.w3.org/TR/rdf11-concepts/#section-skolemization">Section 3.5</a> of [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>] for a fuller discussion. </p>
<p> Suppose G is a graph containing blank nodes and sk is a skolemization mapping from the blank nodes in G to the skolem IRIs which are substituted for them, so that sk(G) is a skolemization of G. Then the semantic relationship between them can be summarized as follows. </p>
<p class="fact"> sk(G) simply entails G (since sk(G) is an instance of G.)</p>
-<p class="fact"> G does not entail sk(G) (since sk(G) contains IRIs not in G.) </p>
-<p class="fact"> For any graph H, if sk(G) entails H then there is a graph H' such that G entails H' and H=sk(H') . </p>
+<p class="fact"> G does not simply entail sk(G) (since sk(G) contains IRIs not in G.) </p>
+<p class="fact"> For any graph H, if sk(G) simply entails H then there is a graph H' such that G entails H' and H=sk(H') . </p>
<p class="fact"> For any graph H which does not contain any of the "new" IRIs introduced into sk(G), sk(G) simply entails H if and only if G simply entails H.
</p>
-<p>The second property means that a graph is not logically <a>equivalent</a> to its skolemization. Nevertheless, they are in a strong sense almost interchangeable, as shown the next two properties. The third property means that even when conclusions are drawn from the skolemized graph which do contain the new vocabulary, these will exactly mirror what could have been derived from the original graph with the original blank nodes in place. The replacement of blank nodes by IRIs does not effectively alter what can be validly derived from the graph, other than by giving new names to what were formerly anonymous entities. The fourth property, which is a consequence of the third, clearly shows that in some sense a skolemization of G can "stand in for" G as far as entailments are concerned. Using sk(G) instead of G will not affect any entailments which do not involve the new skolem vocabulary. </p>
+<p>The second property means that a graph is not logically <a class="internalDFN" href="#dfn-equivalent">equivalent</a> to its skolemization. Nevertheless, they are in a strong sense almost interchangeable, as shown the next two properties. The third property means that even when conclusions are drawn from the skolemized graph which do contain the new vocabulary, these will exactly mirror what could have been derived from the original graph with the original blank nodes in place. The replacement of blank nodes by IRIs does not effectively alter what can be validly derived from the graph, other than by giving new names to what were formerly anonymous entities. The fourth property, which is a consequence of the third, clearly shows that in some sense a skolemization of G can "stand in for" G as far as entailments are concerned. Using sk(G) instead of G will not affect any entailments which do not involve the new skolem vocabulary. </p>
</section>
-<section id="literals-and-datatypes" rel="bibo:chapter" resource="#datatypes" typeof="bibo:Chapter"><!--OddPage--><h2 id="datatypes"><span class="secno">7. </span>Literals and datatypes</h2>
+<section id="literals-and-datatypes" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter"><!--OddPage--><h2 role="heading" aria-level="1" id="datatypes"><span class="secno">7. </span>Literals and datatypes</h2>
<p class="changenote"> In the 2004 RDF 1.0 specification, datatype D-entailment was defined as a <a class="internalDFN" href="#dfn-semantic-extension">semantic extension</a> of RDFS-entailment. Here it is defined as a direct extension to basic RDF. This is more in conformity with actual usage, where RDF with datatypes is widely used without the RDFS vocabulary. If there is a need to distinguish this from the 2004 RDF 1.0 terminology, the longer phrasing "simple D-entailment" or "simple datatype entailment" should be used rather than "D-entailment". </p>
-<p> Datatypes are <a class="internalDFN" href="#dfn-identify" title="identify">identified</a> by IRIs. Interpretations will vary according to which IRIs they recognize as denoting datatypes. We describe this using a parameter D on interpretations. where D is the set of <dfn id="dfn-recognize">recognize</dfn><strong>d</strong> datatype IRIs. We assume that a recognized IRI <a class="internalDFN" href="#dfn-identify" title="identify">identifies</a> a unique datatype wherever it occurs, and the semantics requires that it refers to this identified datatype. The exact mechanism by which an IRI <a class="internalDFN" href="#dfn-identify" title="identify">identifies</a> a datatype IRI is considered to be external to the semantics. RDF processors which are not able to determine which datatype is identifier by an IRI cannot <a class="internalDFN" href="#dfn-recognize">recognize</a> that IRI, and should treat any literals type with that IRI as unknown names. </p>
-
-<p class="changenote">In the 2004 RDF 1.0 specification, the semantics of datatypes referred to datatype maps. The current treatment subsumes datatype maps into the interpretation mapping on recognized IRIs.</p>
+<p> Datatypes are <a class="internalDFN" href="#dfn-identify" title="identify">identified</a> by IRIs. Interpretations will vary according to which IRIs they recognize as denoting datatypes. We describe this using a parameter D on simple interpretations. where D is the set of <dfn id="dfn-recognize">recognize</dfn><strong>d</strong> datatype IRIs. We assume that a recognized IRI <a class="internalDFN" href="#dfn-identify" title="identify">identifies</a> a unique datatype wherever it occurs, and the semantics requires that it refers to this identified datatype. The exact mechanism by which an IRI <a class="internalDFN" href="#dfn-identify" title="identify">identifies</a> a datatype IRI is considered to be external to the semantics. RDF processors which are not able to determine which datatype is identified by an IRI cannot <a class="internalDFN" href="#dfn-recognize">recognize</a> that IRI, and should treat any literals with that IRI as their datatype IRI as unknown names. </p>
-<p>RDF literals and datatypes are fully described in <a href="http://www.w3.org/TR/rdf11-concepts/#section-Datatypes"> Section 5</a> of [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>]. In summary: RDF literals are either language-tagged strings, or datatyped literals which
-combine a string and an IRI <a class="internalDFN" href="#dfn-identify">identify</a>ing a datatype. A datatype is understood to define a partial mapping, called the <dfn id="dfn-lexical-to-value-mapping">lexical-to-value mapping</dfn>, from character strings to values. The function <dfn id="dfn-l2v">L2V</dfn> maps datatypes to their lexical-to-value mapping. A literal with datatype d denotes the value obtained by applying this mapping to the character string sss: L2V(d)(sss). If the lexical-to-value mapping gives no value for the literal string, then the literal has no referent. The <dfn id="dfn-value-space">value space</dfn> of a datatype is the range of the <a class="internalDFN" href="#dfn-lexical-to-value-mapping">lexical-to-value mapping</a>. Every literal with that type either refers to a value in the value space of the type, or fails to refer at all. An <dfn id="dfn-ill-typed">ill-typed</dfn> literal is one whose datatype IRI is <a class="internalDFN" href="#dfn-recognize">recognize</a>d, but whose character string is assigned no value by the <a class="internalDFN" href="#dfn-lexical-to-value-mapping">lexical-to-value mapping</a> for that datatype. </p>
+<p class="changenote">In the 2004 RDF 1.0 specification, the semantics of datatypes referred to datatype maps. The current treatment subsumes datatype maps into the interpretation mapping on recognized IRIs.The <dfn id="dfn-datatype-map">datatype map</dfn> corresponding to D is exactly the restriction of a D-interpretation mapping to the set D of recognized datatypes. The 2004 definitions permitted "non-standard" datatype maps which map IRIs to datatypes they do not <a class="internalDFN" href="#dfn-identify">identify</a> (such as one that maps the IRI '<code>http://www.w3.org/2001/XMLSchema#decimal</code>' to the datatype identified by <code>http://www.w3.org/2001/XMLSchema#gYearMonth</code> ). Semantic extensions based on such non-standard mappings are not sanctioned by this specification.</p>
-<p> RDF processors are not <em title="REQUIRED" class="rfc2119">REQUIRED</em> to <a class="internalDFN" href="#dfn-recognize">recognize</a> any datatype IRIs other than <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> and <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a>, but when IRIs listed in <a href="http://www.w3.org/TR/rdf11-concepts/#section-Datatypes">Section 5</a> of [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>] are <a class="internalDFN" href="#dfn-recognize">recognize</a>d, they <em title="MUST" class="rfc2119">MUST</em> be interpreted as described there, and when the IRI <code>rdf:PlainLiteral</code> is <a class="internalDFN" href="#dfn-recognize">recognize</a>d, it <em title="MUST" class="rfc2119">MUST</em> be interpreted to refer to the datatype defined in [<cite><a href="#bib-RDF-PLAIN-LITERAL" class="bibref">RDF-PLAIN-LITERAL</a></cite>]. RDF processors <em title="MAY" class="rfc2119">MAY</em> recognize other datatype IRIs, but when other datatype IRIs are <a class="internalDFN" href="#dfn-recognize">recognize</a>d, the mapping between a <a class="internalDFN" href="#dfn-recognize">recognize</a>d IRI and the datatype it refers to <em title="MUST" class="rfc2119">MUST</em> be specified unambiguously, and <em title="MUST" class="rfc2119">MUST</em> be fixed during all RDF transformations or manipulations.</p>
+<p>RDF literals and datatypes are fully described in <a href="http://www.w3.org/TR/rdf11-concepts/#section-Datatypes"> Section 5</a> of [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>]. In summary: RDF literals are either language-tagged strings, or datatyped literals which
+combine a string and an IRI <a class="internalDFN" href="#dfn-identify">identify</a>ing a datatype. A datatype is understood to define a partial mapping, called the <dfn id="dfn-lexical-to-value-mapping">lexical-to-value mapping</dfn>, from a lexical space (a set of character strings) to values. The function <dfn id="dfn-l2v">L2V</dfn> maps datatypes to their lexical-to-value mapping. A literal with datatype d denotes the value obtained by applying this mapping to the character string sss: L2V(d)(sss). If the literal string is not in the lexical space, so that the lexical-to-value mapping gives no value for the literal string, then the literal has no referent. The <dfn id="dfn-value-space">value space</dfn> of a datatype is the range of the <a class="internalDFN" href="#dfn-lexical-to-value-mapping">lexical-to-value mapping</a>. Every literal with that type either refers to a value in the value space of the type, or fails to refer at all. An <dfn id="dfn-ill-typed">ill-typed</dfn> literal is one whose datatype IRI is <a class="internalDFN" href="#dfn-recognize">recognize</a>d, but whose character string is assigned no value by the <a class="internalDFN" href="#dfn-lexical-to-value-mapping">lexical-to-value mapping</a> for that datatype. </p>
+
+<p> RDF processors are not required to <a class="internalDFN" href="#dfn-recognize">recognize</a> any datatype IRIs other than <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> and <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a>, but when IRIs listed in <a href="http://www.w3.org/TR/rdf11-concepts/#section-Datatypes">Section 5</a> of [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>] are <a class="internalDFN" href="#dfn-recognize">recognize</a>d, they <em title="MUST" class="rfc2119">MUST</em> be interpreted as described there, and when the IRI <code>rdf:PlainLiteral</code> is <a class="internalDFN" href="#dfn-recognize">recognize</a>d, it <em title="MUST" class="rfc2119">MUST</em> be interpreted to refer to the datatype defined in [<cite><a href="#bib-RDF-PLAIN-LITERAL" class="bibref">RDF-PLAIN-LITERAL</a></cite>]. RDF processors <em title="MAY" class="rfc2119">MAY</em> recognize other datatype IRIs, but when other datatype IRIs are <a class="internalDFN" href="#dfn-recognize">recognize</a>d, the mapping between a <a class="internalDFN" href="#dfn-recognize">recognize</a>d IRI and the datatype it refers to <em title="MUST" class="rfc2119">MUST</em> be specified unambiguously, and <em title="MUST" class="rfc2119">MUST</em> be fixed during all RDF transformations or manipulations.</p>
<p>Literals with <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> as their datatype are an exceptional case which are given a special treatment. The IRI <code>rdf:langString</code> is classified as a datatype IRI, and interpreted to refer to a datatype, even though no L2V mapping is defined for it. The value space of <code>rdf:langString</code> is the set of all pairs of a string with a language tag. The semantics of literals with this as their type are given below. </p>
<p>RDF literal syntax allows any IRI to be used in a typed literal, even when it is not <a class="internalDFN" href="#dfn-recognize">recognize</a>d as referring to a datatype. Literals with such an "unknown" datatype IRI, which is not in the set of <a class="internalDFN" href="#dfn-recognize">recognize</a>d datatypes, <em title="SHOULD NOT" class="rfc2119">SHOULD NOT</em> be treated as errors, although RDF applications <em title="MAY" class="rfc2119">MAY</em> issue a warning. Such literals <em title="SHOULD" class="rfc2119">SHOULD</em> be treated like IRIs and assumed to denote some thing in the universe IR. RDF processors which fail to <a class="internalDFN" href="#dfn-recognize">recognize</a> a datatype IRI will not be able to detect some entailments which are visible to one which does. For example, the fact that </p><p><code>ex:a ex:p "20.0000"^^xsd:decimal .</code></p><p>entails </p><p><code>ex:a ex:p "20.0"^^xsd:decimal .</code></p><p>will not be visible to a processor which does not <a class="internalDFN" href="#dfn-recognize">recognize</a> the datatype IRI <code>xsd:decimal</code>.</p>
-<section rel="bibo:chapter" resource="#D_interpretations" typeof="bibo:Chapter" id="D_interpretations"><h3><span class="secno">7.1 </span>D-interpretations</h3>
-<p>Let D be a set of IRIs <a class="internalDFN" href="#dfn-identify">identify</a>ing datatypes. A <dfn id="dfn-simple-d-interpretation">(simple) D-interpretation</dfn> is a <a class="internalDFN" href="#dfn-simple-interpretation">simple interpretation</a> which satisfies the following conditions:</p>
+<section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" id="D_interpretations"><h3 id="h3_D_interpretations" role="heading" aria-level="2"><span class="secno">7.1 </span>D-interpretations</h3>
+<p>Let D be a set of IRIs <a class="internalDFN" href="#dfn-identify">identify</a>ing datatypes. A <strong>(simple)</strong> <dfn id="dfn-d-interpretation">D-interpretation</dfn> is a <a class="internalDFN" href="#dfn-simple-interpretation">simple interpretation</a> which satisfies the following conditions:</p>
<div class="tabletitle">Semantic conditions for datatyped literals.</div>
<table border="1">
@@ -690,7 +707,7 @@
<p>If the literal is <a class="internalDFN" href="#dfn-ill-typed">ill-typed</a> then the L2V(I(aaa)) mapping has no value, and so the literal cannot denote anything. In this case, any triple containing the literal must be false. Thus, any triple, and hence any graph, containing an <a class="internalDFN" href="#dfn-ill-typed">ill-typed</a> literal will be <a class="internalDFN" href="#dfn-d-unsatisfiable">D-unsatisfiable</a>, i.e. false in every D-interpretation. This applies only to literals typed with recognized datatype IRIs in D; literals with an unrecognized type IRI are not <a class="internalDFN" href="#dfn-ill-typed">ill-typed</a> and cannot give rise to a <a class="internalDFN" href="#dfn-d-unsatisfiable">D-unsatisfiable</a> graph. </p>
-<p>The built-in RDF datatype <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> has no <a class="internalDFN" href="#dfn-ill-typed">ill-typed</a> literals. Any syntactically legal literal with this type will denote a value in every RDF interpretation. The only ill-typed literals of type <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a> are those containing a Unicode code point which does not match the <a href="http://www.w3.org/TR/xml11/#NT-Char"><em>Char</em> production</a> in [<cite><a href="#bib-XML10" class="bibref">XML10</a></cite>]. Such strings cannot be written in an XML-compatible surface syntax.
+<p>The special datatype <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> has no <a class="internalDFN" href="#dfn-ill-typed">ill-typed</a> literals. Any syntactically legal literal with this type will denote a value in every D-interpretation where D included <code>rdf:langString</code>. The only ill-typed literals of type <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a> are those containing a Unicode code point which does not match the <a href="http://www.w3.org/TR/xml11/#NT-Char"><em>Char</em> production</a> in [<cite><a href="#bib-XML10" class="bibref">XML10</a></cite>]. Such strings cannot be written in an XML-compatible surface syntax.
</p>
@@ -703,8 +720,8 @@
</section>
-<section id="datatype-entailment" rel="bibo:chapter" resource="#D_entailment" typeof="bibo:Chapter">
-<h3 id="D_entailment"><span class="secno">7.2 </span>Datatype entailment</h3>
+<section id="datatype-entailment" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
+<h3 role="heading" aria-level="2" id="D_entailment"><span class="secno">7.2 </span>Datatype entailment</h3>
<p>A graph is (simply) <dfn id="dfn-d-satisfiable">D-satisfiable</dfn> or <dfn id="dfn-satisfiable-recognizing-d">satisfiable recognizing D</dfn> when it has the value true in some D-interpretation, and a graph S (simply) <dfn id="dfn-d-entails">D-entails</dfn> or <dfn id="dfn-entails-recognizing-d">entails recognizing D</dfn> a graph G when every D-interpretation which satisfies S also D-satisfies G.</p>
@@ -718,8 +735,8 @@
-<section id="patterns-of-datatype-entailment-informative" rel="bibo:chapter" resource="#datatype_entailment_patterns" typeof="bibo:Chapter" class="informative"> <h4 id="datatype_entailment_patterns"><span class="secno">7.2.1 </span>Patterns of datatype entailment (Informative)</h4><p><em>This section is non-normative.</em></p>
-<p>Unlike <a class="internalDFN" href="#dfn-simply-entails" title="simply entails">simple entailment</a>, it is not possible to give a single syntactic criterion to detect all D-entailments, which
+<section id="patterns-of-datatype-entailment-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative"> <h4 role="heading" aria-level="3" id="datatype_entailment_patterns"><span class="secno">7.2.1 </span>Patterns of datatype entailment (Informative)</h4><p><em>This section is non-normative.</em></p>
+<p>Unlike <a class="internalDFN" href="#dfn-entail" title="entail">simple entailment</a>, it is not possible to give a single syntactic criterion to detect all D-entailments, which
can hold because of particular properties of the lexical-to-value mappings of the <a class="internalDFN" href="#dfn-recognize">recognize</a>d datatypes. For example, if D contains <code>xsd:decimal</code> then </p>
<p><code>ex:a ex:p "25.0"^^xsd:decimal .</code></p>
@@ -742,29 +759,48 @@
</section>
</section>
-<section id="rdf-interpretations" rel="bibo:chapter" resource="#rdf_d_interpretations" typeof="bibo:Chapter"><!--OddPage--><h2 id="rdf_d_interpretations"><span class="secno">8. </span>RDF Interpretations</h2>
- <p>RDF interpretations impose extra semantic conditions on <code>xsd:string</code> and part of the infinite
- set of IRIs with the namespace prefix <code>rdf:</code> .
+<section id="rdf-interpretations" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter"><!--OddPage--><h2 role="heading" aria-level="1" id="rdf_d_interpretations"><span class="secno">8. </span>RDF Interpretations</h2>
+ <p>RDF interpretations impose extra semantic conditions on <code>xsd:string</code> and part of the infinite
+ set of IRIs with the namespace prefix <code>rdf:</code> .
-</p><p>An <dfn id="dfn-rdf-interpretation">RDF interpretation</dfn> <strong>recognizing D</strong> is a <a>D-interpretation</a> I where D includes <code>rdf:langString</code> and <code>xsd:string</code>, and which satisfies:</p>
-<div class="tabletitle">RDF semantic conditions.</div>
+</p><div>
+ <table border="1">
+ <tbody>
+ <tr>
+ <td><dfn id="dfn-rdf-vocabulary">RDF vocabulary</dfn></td>
+ </tr>
+
+ <tr>
+ <td><code>rdf:type rdf:subject rdf:predicate rdf:object
+ rdf:first rdf:rest rdf:value rdf:nil
+ rdf:List rdf:langString rdf:Property rdf:_1 rdf:_2
+ ...
+</code></td>
+ </tr>
+ </tbody>
+ </table>
+ </div>
+
+
+<p>An <dfn id="dfn-rdf-interpretation">RDF interpretation</dfn> <strong>recognizing D</strong> is a <a class="internalDFN" href="#dfn-d-interpretation">D-interpretation</a> I where D includes <code>rdf:langString</code> and <code>xsd:string</code>, and which satisfies:</p>
+<div class="tabletitle">RDF semantic conditions.</div>
<table border="1">
<tbody>
- <tr>
- <td class="semantictable"><a id="rdfsemcond1"></a>x is
+ <tr>
+ <td class="semantictable" id="rdfsemcond1">x is
in IP if and only if <x, I(<code>rdf:Property</code>)> is in IEXT(I(<code>rdf:type</code>))</td>
</tr>
-<tr><td class="semantictable"><a id="rdfsemcond3">For every IRI aaa in D, < x, I(aaa) > is in IEXT(I(<code>rdf:type</code>)) if and only if x is in the value space of I(aaa)</a></td></tr>
+<tr><td class="semantictable" id="rdfsemcond3">For every IRI aaa in D, < x, I(aaa) > is in IEXT(I(<code>rdf:type</code>)) if and only if x is in the value space of I(aaa)</td></tr>
-
+
</tbody>
</table>
- <p>and satisfies every triple in the following infinite set:</p>
- <div class="tabletitle">RDF axioms.</div>
+ <p>and satisfies every triple in the following infinite set:</p>
+ <div class="tabletitle">RDF axioms.</div>
<table border="1">
<tbody><tr>
- <td class="ruletable"><a id="RDF_axiomatic_triples"> </a><code>rdf:type rdf:type rdf:Property .<br>
+ <td class="ruletable" id="RDF_axiomatic_triples"><code>rdf:type rdf:type rdf:Property .<br>
rdf:subject rdf:type rdf:Property .<br>
rdf:predicate rdf:type rdf:Property .<br>
rdf:object rdf:type rdf:Property .<br>
@@ -776,12 +812,12 @@
rdf:_2 rdf:type rdf:Property .<br>
... <br>
</code>
-
+
</td>
</tr>
</tbody></table>
-<p>RDF imposes no particular normative meanings on the rest of the RDF vocabulary. <a>Appendix D</a> describes the intended uses of some of this vocabulary.</p>
+<p>RDF imposes no particular normative meanings on the rest of the RDF vocabulary. <a href="#whatnot">Appendix D</a> describes the intended uses of some of this vocabulary.</p>
<p>The datatype IRIs <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> and <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a> <em title="MUST" class="rfc2119">MUST</em> be <a class="internalDFN" href="#dfn-recognize">recognize</a>d by all RDF interpretations. </p>
@@ -789,34 +825,34 @@
<p>Two other datatypes <a href="http://www.w3.org/TR/rdf11-concepts/#section-XMLLiteral"><code>rdf:XMLLiteral</code></a> and <a href="http://www.w3.org/TR/rdf11-concepts/#section-html"><code>rdf:HTML</code></a> are defined in [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>]. RDF-D interpretations <em title="MAY" class="rfc2119">MAY</em> fail to <a class="internalDFN" href="#dfn-recognize">recognize</a> these datatypes. </p>
-<section id="rdf-entailment" rel="bibo:chapter" resource="#rdf_entail" typeof="bibo:Chapter">
+<section id="rdf-entailment" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
-<h3 id="rdf_entail"><span class="secno">8.1 </span>RDF entailment</h3>
+<h3 role="heading" aria-level="2" id="rdf_entail"><span class="secno">8.1 </span>RDF entailment</h3>
-<p>S <dfn id="dfn-rdf-entail">RDF entail</dfn><strong>s</strong> E <strong>recognizing D</strong> when every <a>RDF interpretation recognizing D</a> which satisfies S also satisfies E. When D is {<code>rdf:langString</code>, <code>xsd:string</code>} then we simply say S <strong>RDF entails</strong> E. </p>
+<p>S <dfn id="dfn-rdf-entail">RDF entail</dfn><strong>s</strong> E <strong>recognizing D</strong> when every <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a> recognizing D which satisfies S also satisfies E. When D is {<code>rdf:langString</code>, <code>xsd:string</code>} then we simply say S <strong>RDF entails</strong> E. E is <dfn id="dfn-rdf-unsatisfiable">RDF unsatisfiable</dfn><strong> (recognizing D)</strong> when it has no satisfying <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a> (recognizing D).</p>
-<p>The properties of <a>simple entailment</a> described earlier do not all apply to <a class="internalDFN" href="#dfn-rdf-entail">RDF entail</a>ment. For example, all the RDF axioms are true in every <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a>, and so are <a class="internalDFN" href="#dfn-rdf-entail">RDF entail</a>ed by the empty graph, contradicting <a class="internalDFN" href="#dfn-interpolation">interpolation</a> for RDF entailment. </p>
+<p>The properties of simple entailment described earlier do not all apply to <a class="internalDFN" href="#dfn-rdf-entail">RDF entail</a>ment. For example, all the RDF axioms are true in every <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a>, and so are <a class="internalDFN" href="#dfn-rdf-entail">RDF entail</a>ed by the empty graph, contradicting <a class="internalDFN" href="#dfn-interpolation">interpolation</a> for RDF entailment. </p>
-<section id="patterns-of-rdf-entailment-informative" rel="bibo:chapter" resource="#rdf_entailment_patterns" typeof="bibo:Chapter" class="informative"><h4 id="rdf_entailment_patterns"><span class="secno">8.1.1 </span>Patterns of RDF entailment (Informative)</h4><p><em>This section is non-normative.</em></p>
-<p> The last semantic condition in the above table gives the following entailment pattern for <a class="internalDFN" href="#dfn-recognize">recognize</a>d datatype IRIs: </p>
+<section id="patterns-of-rdf-entailment-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative"><h4 role="heading" aria-level="3" id="rdf_entailment_patterns"><span class="secno">8.1.1 </span>Patterns of RDF entailment (Informative)</h4><p><em>This section is non-normative.</em></p>
+<p> The last semantic condition in the above table gives the following entailment pattern for <a class="internalDFN" href="#dfn-recognize">recognize</a>d datatype IRIs: </p>
-<div class="tabletitle">RDF entailment pattern.</div>
+<div class="tabletitle">RDF entailment pattern.</div>
<table border="1">
<tbody>
- <tr>
+ <tr>
<th> </th>
<th><strong>if S contains</strong></th>
<th><strong>then S RDF entails, recognizing D</strong></th>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfd1">rdfD1</dfn></td>
<td class="othertable"> xxx aaa <code>"</code>sss<code>"^^</code>ddd <code>.</code> <br>
for ddd in D</td>
<td class="othertable">xxx aaa _:nnn <code>.</code><br>
_:nnn <code>rdf:type</code> ddd <code>.</code></td>
</tr>
-
+
</tbody>
</table>
<p>Note, this is valid even when the literal is <a class="internalDFN" href="#dfn-ill-typed">ill-typed</a>, since an unsatisfiable graph entails any triple.</p>
@@ -833,19 +869,19 @@
<table border="1">
<tbody>
- <tr>
+ <tr>
<th> </th>
<th><strong>if S contains</strong></th>
<th><strong>then S RDF entails, recognizing D</strong></th>
</tr>
-
+
<tr>
<td class="othertable"><dfn id="dfn-rdfd2">rdfD2</dfn></td>
<td class="othertable">xxx aaa yyy <code>.</code></td>
<td class="othertable">aaa <code>rdf:type rdf:Property .</code> </td>
</tr>
-
-
+
+
</tbody>
</table>
@@ -865,7 +901,7 @@
<p> recognizing {<code>xsd:boolean</code>}.</p>
-<p>In addition, the semantic conditions on value spaces may produce other unsatisfiable graphs. For example, when D contains <code>xsd:integer</code> and <code>xsd:boolean</code>, then the following is <a>RDF unsatisfiable</a> recognizing D:</p>
+<p>In addition, the semantic conditions on value spaces may produce other unsatisfiable graphs. For example, when D contains <code>xsd:integer</code> and <code>xsd:boolean</code>, then the following is <a class="internalDFN" href="#dfn-rdf-unsatisfiable">RDF unsatisfiable</a> recognizing D:</p>
<p><code>_:x rdf:type xsd:boolean .<br>
_:x rdf:type xsd:integer . </code></p>
@@ -873,9 +909,9 @@
</section>
</section>
</section>
-<section id="rdfs-interpretations" rel="bibo:chapter" resource="#rdfs_interpretations" typeof="bibo:Chapter"><!--OddPage--><h2 id="rdfs_interpretations"><span class="secno">9. </span>RDFS Interpretations</h2>
+<section id="rdfs-interpretations" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter"><!--OddPage--><h2 role="heading" aria-level="1" id="rdfs_interpretations"><span class="secno">9. </span>RDFS Interpretations</h2>
<p>RDF Schema [<cite><a href="#bib-RDF-SCHEMA" class="bibref">RDF-SCHEMA</a></cite>]
- extends RDF to a larger vocabulary
+ extends RDF to a larger vocabulary
with more complex semantic constraints:</p>
<div>
@@ -895,31 +931,31 @@
</tbody>
</table>
</div>
-<p>(<code>rdfs:comment</code>,<code> rdfs:seeAlso</code>, <code>rdfs:isDefinedBy</code>
- and <code>rdfs:label</code> are included here because some constraints which
- apply to their use can be stated using <code>rdfs:domain</code>,<code> rdfs:range</code>
- and <code>rdfs:subPropertyOf</code>. Other than this, the formal semantics does
+<p>(<code>rdfs:comment</code>,<code> rdfs:seeAlso</code>, <code>rdfs:isDefinedBy</code>
+ and <code>rdfs:label</code> are included here because some constraints which
+ apply to their use can be stated using <code>rdfs:domain</code>,<code> rdfs:range</code>
+ and <code>rdfs:subPropertyOf</code>. Other than this, the formal semantics does
not constrain their meanings.)</p>
-<p>It is convenient to state the RDFS semantics
- in terms of a new semantic construct, a <dfn id="dfn-class">class</dfn>, i.e. a resource which represents
- a set of things in the universe which all have that class as a value of their
- <code>rdf:type</code> property. <a class="internalDFN" href="#dfn-class">Class</a>es are defined to be things of type <code>rdfs:Class</code>,
- and the set of all classes in an interpretation will be called IC.
- The semantic conditions are stated in terms of a mapping ICEXT (for the <em>C</em>lass
- <em>Ext</em>ension in I) from IC to the set of subsets of IR.</p><p> A class may have an
+<p>It is convenient to state the RDFS semantics
+ in terms of a new semantic construct, a <dfn id="dfn-class">class</dfn>, i.e. a resource which represents
+ a set of things in the universe which all have that class as a value of their
+ <code>rdf:type</code> property. <a class="internalDFN" href="#dfn-class">Class</a>es are defined to be things of type <code>rdfs:Class</code>,
+ and the set of all classes in an interpretation will be called IC.
+ The semantic conditions are stated in terms of a mapping ICEXT (for the <em>C</em>lass
+ <em>Ext</em>ension in I) from IC to the set of subsets of IR.</p><p> A class may have an
empty class extension. Two different classes can have the same class extension.
- The class extension of <code>rdfs:Class</code> contains the class <code>rdfs:Class</code>.
+ The class extension of <code>rdfs:Class</code> contains the class <code>rdfs:Class</code>.
</p>
-
-<p> An <dfn id="dfn-rdfs-interpretation">RDFS interpretation</dfn> (<strong>recognizing D</strong>) is an <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a> (recognizing D) I
+
+<p> An <dfn id="dfn-rdfs-interpretation">RDFS interpretation</dfn> (<strong>recognizing D</strong>) is an <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a> (recognizing D) I
which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples. </p>
-
+
<div class="tabletitle">RDFS semantic conditions.</div>
<table border="1">
- <tbody><tr>
-
- <td class="semantictable"> <p><a id="rdfssemcond1"></a>ICEXT(y) is defined to be { x : < x,y > is in IEXT(I(<code>rdf:type</code>)) }</p>
+ <tbody><tr>
+
+ <td class="semantictable" id="rdfssemcond1"> <p>ICEXT(y) is defined to be { x : < x,y > is in IEXT(I(<code>rdf:type</code>)) }</p>
<p>IC is defined to be ICEXT(I(<code>rdfs:Class</code>))</p>
<p>LV is defined to be ICEXT(I(<code>rdfs:Literal</code>))</p>
<p>ICEXT(I(<code>rdfs:Resource</code>)) = IR</p>
@@ -928,56 +964,56 @@
<p>for every IRI aaa in D, I(aaa) is in ICEXT(I(<code>rdfs:Datatype</code>)) </p>
</td>
</tr>
- <tr>
-
- <td class="semantictable"> <p><a id="rdfssemcond2"></a>If
- < x,y > is in IEXT(I(<code>rdfs:domain</code>)) and < u,v > is
+ <tr>
+
+ <td class="semantictable" id="rdfssemcond2"> <p>If
+ < x,y > is in IEXT(I(<code>rdfs:domain</code>)) and < u,v > is
in IEXT(x) then u is in ICEXT(y)</p></td>
</tr>
- <tr>
-
- <td class="semantictable"> <p><a id="rdfssemcond3"></a>If
- < x,y > is in IEXT(I(<code>rdfs:range</code>)) and < u,v > is
+ <tr>
+
+ <td class="semantictable" id="rdfssemcond3"> <p>If
+ < x,y > is in IEXT(I(<code>rdfs:range</code>)) and < u,v > is
in IEXT(x) then v is in ICEXT(y)</p></td>
</tr>
- <tr>
-
- <td class="semantictable"><p><a id="rdfssemcond4"></a>IEXT(I(<code>rdfs:subPropertyOf</code>))
+ <tr>
+
+ <td class="semantictable" id="rdfssemcond4"><p>IEXT(I(<code>rdfs:subPropertyOf</code>))
is transitive and reflexive on IP</p></td>
</tr>
- <tr>
-
- <td class="semantictable"> <p><a id="rdfssemcond5"></a>If
- <x,y> is in IEXT(I(<code>rdfs:subPropertyOf</code>)) then x and
+ <tr>
+
+ <td class="semantictable" id="rdfssemcond5"> <p>If
+ <x,y> is in IEXT(I(<code>rdfs:subPropertyOf</code>)) then x and
y are in IP and IEXT(x) is a subset of IEXT(y)</p></td>
</tr>
- <tr>
-
- <td class="semantictable"><p><a id="rdfssemcond6"></a>If
+ <tr>
+
+ <td class="semantictable" id="rdfssemcond6"><p>If
x is in IC then < x, I(<code>rdfs:Resource</code>) > is in IEXT(I(<code>rdfs:subClassOf</code>))</p></td>
</tr>
- <tr>
+ <tr>
- <td class="semantictable"><p><a id="rdfssemcond8"></a>IEXT(I(<code>rdfs:subClassOf</code>))
+ <td class="semantictable" id="rdfssemcond8"><p>IEXT(I(<code>rdfs:subClassOf</code>))
is transitive and reflexive on IC</p></td>
</tr>
<tr>
- <td class="semantictable"> <p><a id="rdfssemcond7"></a>If
- < x,y > is in IEXT(I(<code>rdfs:subClassOf</code>)) then x and y are
+ <td class="semantictable" id="rdfssemcond7"> <p>If
+ < x,y > is in IEXT(I(<code>rdfs:subClassOf</code>)) then x and y are
in IC and ICEXT(x) is a subset of ICEXT(y)</p></td>
</tr>
-
- <tr>
- <td class="semantictable"><p><a id="rdfssemcond9"></a>If
+
+ <tr>
+ <td class="semantictable" id="rdfssemcond9"><p>If
x is in ICEXT(I(<code>rdfs:ContainerMembershipProperty</code>)) then:<br>
< x, I(<code>rdfs:member</code>) > is in IEXT(I(<code>rdfs:subPropertyOf</code>))<br>
</p></td>
</tr>
- <tr>
-
- <td class="semantictable"><p><a id="rdfssemcond10"></a>If
- x is in ICEXT(I(<code>rdfs:Datatype</code>)) then <span>< x,
+ <tr>
+
+ <td class="semantictable" id="rdfssemcond10"><p>If
+ x is in ICEXT(I(<code>rdfs:Datatype</code>)) then <span>< x,
I(<code>rdfs:Literal</code>) > is in IEXT(I(<code>rdfs:subClassOf</code>))</span></p></td>
</tr>
</tbody></table>
@@ -985,15 +1021,15 @@
-
- <p><a id="RDFS_axiomatic_triples"> </a>
+
+ <p>
</p>
<div class="tabletitle">RDFS axiomatic triples.</div>
- <table border="1">
-
+ <table id="RDFS_axiomatic_triples" border="1">
+
<tbody><tr>
-
-
+
+
<td class="ruletable"> <code>rdf:type rdfs:domain rdfs:Resource .<br>
rdfs:domain rdfs:domain rdf:Property .<br>
rdfs:range rdfs:domain rdf:Property .<br>
@@ -1035,7 +1071,7 @@
<br>
rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso .<br>
<br>
-
+
rdfs:Datatype rdfs:subClassOf rdfs:Class .<br>
<br>
rdf:_1 rdf:type rdfs:ContainerMembershipProperty .<br>
@@ -1046,21 +1082,21 @@
rdf:_2 rdfs:range rdfs:Resource . <br>
</code>... <br> </td>
</tr>
-
+
</tbody></table>
<p class="changenote">In the 2004 RDF 1.0 semantics, LV was defined as part of a simple interpretation structure, and the definition given here was a constraint. </p>
-<p>Since I is an <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a>, the first condition implies that IP
+<p>Since I is an <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a>, the first condition implies that IP
= ICEXT(I(<code>rdf:Property</code>)).</p>
<p>The semantic conditions on <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a>s, together with the RDFS conditions on ICEXT, mean that every <a class="internalDFN" href="#dfn-recognize">recognize</a>d datatype can be treated as a class whose extension is the value space of the datatype, and every literal with that datatype either fails to refer, or refers to a value in that class.</p>
<p>When using RDFS semantics, the referents of all <a class="internalDFN" href="#dfn-recognize">recognize</a>d datatype IRIs can be considered to be in the <a class="internalDFN" href="#dfn-class">class</a> <code>rdfs:Datatype</code>. </p>
-<p>The axioms and conditions listed above have some redundancy. For example, all but one
- of the RDF axiomatic triples can be derived from the RDFS axiomatic triples
+<p>The axioms and conditions listed above have some redundancy. For example, all but one
+ of the RDF axiomatic triples can be derived from the RDFS axiomatic triples
and the semantic conditions on ICEXT,<code> rdfs:domain</code> and <code>rdfs:range</code>. </p>
-<p> Other triples which must be true in all rdfs-interpretations
+<p> Other triples which must be true in all RDFS interpretations
include the following. This is not a complete set.</p>
<div class="tabletitle">Some rdfs-valid triples.</div>
<table border="1">
@@ -1094,8 +1130,8 @@
</tbody></table>
<p>RDFS does not partition the universe into disjoint categories of classes, properties and individuals. Anything in the universe can be used as a class or as a property, or both, while retaining its status as an individual which may be in classes and have properties. Thus, RDFS permits classes which contain other classes, classes of properties, properties of classes, etc. As the axiomatic triples above illustrate, it also permits classes which contain themselves and properties which apply to themselves. A property of a class is not necessarily a property of its members, nor vice versa. </p>
-<section id="a-note-on-rdfs-literal-informative" rel="bibo:chapter" resource="#rdfs_literal_note" typeof="bibo:Chapter" class="informative">
-<h3 id="rdfs_literal_note"><span class="secno">9.1 </span>A note on rdfs:Literal (Informative)</h3><p><em>This section is non-normative.</em></p>
+<section id="a-note-on-rdfs-literal-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative">
+<h3 role="heading" aria-level="2" id="rdfs_literal_note"><span class="secno">9.1 </span>A note on rdfs:Literal (Informative)</h3><p><em>This section is non-normative.</em></p>
<p>The class <code>rdfs:Literal</code> is not the class of literals, but rather that of literal values, which may also be referred to by IRIs. For example, LV does not contain the literal <code>"foodle"^^xsd:string</code> but it does contain the string "foodle".</p>
<p>A triple of the form</p>
@@ -1106,102 +1142,102 @@
than a literal. It says that the IRI '<code>ex:a</code>'
refers to a literal value, which is quite possible since literal values are things in the universe. Blank nodes may range over literal values, for the same reason. </p>
</section>
-<section id="rdfs-entailment" rel="bibo:chapter" resource="#rdfs_entailment" typeof="bibo:Chapter">
+<section id="rdfs-entailment" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
-<h3 id="rdfs_entailment"><span class="secno">9.2 </span>RDFS entailment</h3>
+<h3 role="heading" aria-level="2" id="rdfs_entailment"><span class="secno">9.2 </span>RDFS entailment</h3>
<p>S <dfn id="dfn-rdfs-entails">RDFS entails</dfn> E <strong>recognizing D</strong> when every <a class="internalDFN" href="#dfn-rdfs-interpretation">RDFS interpretation</a> recognizing D
which satisfies S also satisfies E.</p>
-<p> Since every <a class="internalDFN" href="#dfn-rdfs-interpretation">RDFS interpretation</a> is an <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a>, if S <a class="internalDFN" href="#dfn-rdfs-entails">RDFS entails</a>
- E then S also <a class="internalDFN" href="#dfn-rdf-entail">RDF entail</a>s E; but RDFS entailment is stronger than RDF entailment.
- Even the empty graph has a large number of RDFS entailments which are not RDF entailments,
+<p> Since every <a class="internalDFN" href="#dfn-rdfs-interpretation">RDFS interpretation</a> is an <a class="internalDFN" href="#dfn-rdf-interpretation">RDF interpretation</a>, if S <a class="internalDFN" href="#dfn-rdfs-entails">RDFS entails</a>
+ E then S also <a class="internalDFN" href="#dfn-rdf-entail">RDF entail</a>s E; but RDFS entailment is stronger than RDF entailment.
+ Even the empty graph has a large number of RDFS entailments which are not RDF entailments,
for example all triples of the form </p>
<p> aaa <code>rdf:type rdfs:Resource .</code></p>
<p>where aaa is an IRI, are true in all RDFS interpretations.</p>
-<section id="patterns-of-rdfs-entailment-informative" rel="bibo:chapter" resource="#rdfs_patterns" typeof="bibo:Chapter" class="informative"> <h4 id="rdfs_patterns"><span class="secno">9.2.1 </span>Patterns of RDFS entailment (Informative)</h4><p><em>This section is non-normative.</em></p>
+<section id="patterns-of-rdfs-entailment-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative"> <h4 role="heading" aria-level="3" id="rdfs_patterns"><span class="secno">9.2.1 </span>Patterns of RDFS entailment (Informative)</h4><p><em>This section is non-normative.</em></p>
<p>RDFS entailment holds for all the following patterns, which correspond closely to the RDFS semantic conditions:</p>
-<div class="title">RDFS entailment patterns.</div>
+<div class="title">RDFS entailment patterns.</div>
<table border="1">
<tbody>
- <tr>
+ <tr>
<th></th>
<th>If S contains:</th>
<th>then S RDFS entails recognizing D:</th>
</tr>
<tr>
<td class="othertable"><dfn id="dfn-rdfs1">rdfs1</dfn></td>
- <td class="othertable">any IRI aaa in D</td>
+ <td class="othertable">any IRI aaa in D</td>
<td class="othertable">aaa <code>rdf:type rdfs:Datatype . </code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs2">rdfs2</dfn></td>
<td class="othertable"> aaa <code>rdfs:domain</code> xxx <code>.</code><br>
yyy aaa zzz <code>.</code></td>
<td class="othertable">yyy <code>rdf:type</code> xxx <code>.</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs3">rdfs3</dfn></td>
<td class="othertable">aaa <code>rdfs:range</code> xxx <code>.</code><br>
yyy aaa zzz <code>.</code></td>
<td class="othertable">zzz <code>rdf:type</code> xxx <code>.</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs4a">rdfs4a</dfn></td>
<td class="othertable">xxx aaa yyy <code>.</code></td>
<td class="othertable">xxx <code>rdf:type rdfs:Resource .</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs4b">rdfs4b</dfn></td>
<td class="othertable">xxx aaa yyy<code>.</code></td>
<td class="othertable">yyy <code>rdf:type rdfs:Resource .</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs5">rdfs5</dfn></td>
<td class="othertable"> xxx <code>rdfs:subPropertyOf</code> yyy <code>.</code><br>
yyy <code>rdfs:subPropertyOf</code> zzz <code>.</code></td>
<td class="othertable">xxx <code>rdfs:subPropertyOf</code> zzz <code>.</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs6">rdfs6</dfn></td>
<td class="othertable">xxx <code>rdf:type rdf:Property .</code></td>
<td class="othertable">xxx <code>rdfs:subPropertyOf</code> xxx <code>.</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs7">rdfs7</dfn></td>
<td class="othertable"> aaa <code>rdfs:subPropertyOf</code> bbb <code>.</code><br>
xxx aaa yyy <code>.</code></td>
<td class="othertable">xxx bbb yyy <code>.</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs8">rdfs8</dfn></td>
<td class="othertable">xxx <code>rdf:type rdfs:Class .</code></td>
<td class="othertable">xxx <code>rdfs:subClassOf rdfs:Resource .</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs9">rdfs9</dfn></td>
<td class="othertable">xxx <code>rdfs:subClassOf</code> yyy <code>.</code><br>
zzz <code>rdf:type</code> xxx <code>.</code></td>
<td class="othertable">zzz <code>rdf:type</code> yyy <code>.</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs10">rdfs10</dfn></td>
<td class="othertable">xxx <code>rdf:type rdfs:Class .</code></td>
<td class="othertable">xxx <code>rdfs:subClassOf</code> xxx <code>.</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs11">rdfs11</dfn></td>
<td class="othertable"> xxx <code>rdfs:subClassOf</code> yyy <code>.</code><br>
yyy <code>rdfs:subClassOf</code> zzz <code>.</code></td>
<td class="othertable">xxx <code>rdfs:subClassOf</code> zzz <code>.</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs12">rdfs12</dfn></td>
<td class="othertable">xxx <code>rdf:type rdfs:ContainerMembershipProperty .</code></td>
<td class="othertable">xxx <code>rdfs:subPropertyOf rdfs:member .</code></td>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-rdfs13">rdfs13</dfn></td>
<td class="othertable">xxx <code>rdf:type rdfs:Datatype .</code></td>
<td class="othertable">xxx <code>rdfs:subClassOf rdfs:Literal .</code></td>
@@ -1219,11 +1255,15 @@
</section>
</section>
</section>
-<section id="rdf-datasets" rel="bibo:chapter" resource="#rdf_datasets" typeof="bibo:Chapter"><!--OddPage--><h2 id="rdf_datasets"><span class="secno">10. </span>RDF Datasets</h2>
+<section id="rdf-datasets" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter"><!--OddPage--><h2 role="heading" aria-level="1" id="rdf_datasets"><span class="secno">10. </span>RDF Datasets</h2>
-<p>An RDF <a href="http://www.w3.org/TR/rdf11-concepts/#section-dataset" class="externalDFN">dataset</a> (see [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>]) is a finite set of RDF graphs each paired with an IRI or blank node called the <strong>graph name</strong>, plus a <strong>default graph</strong>, without a name. Graphs in a single dataset may share blank nodes. The association of graph name IRIs with graphs is used by SPARQL [<cite><a href="#bib-RDF-SPARQL-QUERY" class="bibref">RDF-SPARQL-QUERY</a></cite>] to allow queries to be directed against particular graphs.</p>
+<!--
+<p>An RDF <a href="http://www.w3.org/TR/rdf11-concepts/#section-dataset" class="externalDFN">dataset</a> (see [[!RDF11-CONCEPTS]]) is a finite set of RDF graphs each paired with an IRI or blank node called the <strong>graph name</strong>, plus a <strong>default graph</strong>, without a name. Graphs in a single dataset may share blank nodes. The association of graph name IRIs with graphs is used by SPARQL [[RDF-SPARQL-QUERY]] to allow queries to be directed against particular graphs.</p>
+-->
-<p>Graph names in a dataset may refer to something other than the graph they are paired with. This allows IRI referring to other kinds of entities, such as persons, to be used in a dataset to <a class="internalDFN" href="#dfn-identify">identify</a> graphs of information relevant to the entity <a>denote</a>d by the graph name IRI.</p>
+<p><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-dataset">RDF datasets</a>, defined in RDF Concepts [<cite><a href="#bib-RDF11-CONCEPTS" class="bibref">RDF11-CONCEPTS</a></cite>], package up zero or more named RDF graphs along with a single unnamed, default RDF graph. The graphs in a single dataset may share blank nodes. The association of graph name IRIs with graphs is used by SPARQL [<cite><a href="#bib-RDF-SPARQL-QUERY" class="bibref">RDF-SPARQL-QUERY</a></cite>] to allow queries to be directed against particular graphs.</p>
+
+<p>Graph names in a dataset may refer to something other than the graph they are paired with. This allows IRI referring to other kinds of entities, such as persons, to be used in a dataset to <a class="internalDFN" href="#dfn-identify">identify</a> graphs of information relevant to the entity <a class="internalDFN" href="#dfn-denote">denote</a>d by the graph name IRI.</p>
<p>When a graph name is used inside RDF triples in a dataset it may or may not refer to the graph it names. The semantics does not require, nor should RDF engines presume, without some external reason to do so, that graph names used in RDF triples refer to the graph they name.</p>
@@ -1236,7 +1276,7 @@
<h2 id="appendices">Appendices</h2>
-<section id="entailment-rules-informative" rel="bibo:chapter" resource="#entailment_rules" typeof="bibo:Chapter" class="informative appendix"><!--OddPage--><h2 id="entailment_rules"><span class="secno">A. </span>Entailment rules (Informative)</h2><p><em>This section is non-normative.</em></p>
+<section id="entailment-rules-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative appendix"><!--OddPage--><h2 role="heading" aria-level="1" id="entailment_rules"><span class="secno">A. </span>Entailment rules (Informative)</h2><p><em>This section is non-normative.</em></p>
<p>(<em>This section is based on work described more fully in </em>[<cite><a href="#bib-HORST04" class="bibref">HORST04</a></cite>]<em>, </em>[<cite><a href="#bib-HORST05" class="bibref">HORST05</a></cite>]<em>, which should be consulted for technical details and proofs.</em>) </p>
<p> The RDF and RDFS entailment patterns listed in the above tables can be viewed as left-to-right rules which add the entailed conclusion to a graph. These rule sets can be used to check RDF (or RDFS) entailment between graphs S and E, by the following sequence of operations:</p>
@@ -1245,38 +1285,38 @@
3. Apply the RDF (or RDF and RDFS) inference patterns as rules, adding each conclusion to the graph, to exhaustion; that is, until they generate no new triples. <br>
4. Determine if E has an instance which is a subset of the set, i.e. whether the enlarged set simply entails E.</p>
-<p>This process is clearly <a>correct</a>, in that if it gives a positive result then indeed S does RDF (RDFS) entail E. It is not, however, <a>complete</a>: there are cases of S entailing E which are not detectable by this process. Examples include:</p>
+<p>This process is clearly correct, in that if it gives a positive result then indeed S does RDF (RDFS) entail E. It is not, however, complete: there are cases of S entailing E which are not detectable by this process. Examples include:</p>
<table border="1">
<tbody>
- <tr>
-
+ <tr>
+
<th> </th>
<th>RDF entails</th>
</tr>
-
+
<tr>
-
+
<td class="othertable"><code>ex:a ex:p "string"^^xsd:string .<br>
ex:b ex:q "string"^^xsd:string .</code></td>
<td class="othertable"><code>ex:a ex:p _:b .<br>
ex:b ex:q _:b .<br>
_:b rdf:type xsd:string .</code> </td>
</tr>
-
- <tr>
-
+
+ <tr>
+
<th> </th>
<th>RDFS entails</th>
</tr>
<tr>
-
+
<td class="othertable"><code>ex:a rdfs:subPropertyOf _:b .<br>
_:b rdfs:domain ex:c .<br>
ex:d ex:a ex:e .</code></td>
<td class="othertable"><code>ex:d rdf:type ex:c .</code> </td>
- </tr>
-
+ </tr>
+
</tbody>
</table>
<p> Both of these can be handled by allowing the rules to apply to a generalization of the RDF syntax in which literals may occur in subject position and blank nodes may occur in predicate position. </p>
@@ -1284,21 +1324,21 @@
<!--<p>Define a <dfn>generalized RDF triple</dfn> to be a triple <x, y, z> where x and z can be an IRI, a blank node or a literal, and y can be an IRI or a blank node; and extend this to the rest of RDF, so that a generalized RDF graph is a set of generalized RDF triples. -->
<p>Consider <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-generalized-rdf">generalized RDF triples, graphs, and datasets</a> instead of RDF triples, graphs and datasets (extending the generalization used in [<cite><a href="#bib-HORST04" class="bibref">HORST04</a></cite>] and following exactly the terms used in [<cite><a href="#bib-OWL2-PROFILES" class="bibref">OWL2-PROFILES</a></cite>]). The semantics described in this document applies to the generalization without change, so that the notions of interpretation, satisfiability and entailment can be used freely. Then we can replace the first RDF entailment pattern with the simpler and more direct</p>
-<div class="tabletitle">G-RDF-D entailment pattern.</div>
+<div class="tabletitle">G-RDF-D entailment pattern.</div>
<table border="1">
<tbody>
- <tr>
+ <tr>
<th> </th>
<th><strong>if S contains</strong></th>
<th><strong>then S RDF entails, recognizing D</strong></th>
</tr>
- <tr>
+ <tr>
<td class="othertable"><dfn id="dfn-grdfd1">GrdfD1</dfn></td>
<td class="othertable"> xxx aaa <code>"</code>sss<code>"^^</code>ddd <code>.</code> <br>
for ddd in D</td>
<td class="othertable"><code>"</code>sss<code>"^^</code>ddd <code>rdf:type</code> ddd <code>.</code></td>
</tr>
-
+
</tbody>
</table>
@@ -1325,7 +1365,7 @@
4. Apply the rules <a class="internalDFN" href="#dfn-grdfd1">GrdfD1</a> and <a class="internalDFN" href="#dfn-rdfd2">rdfD2</a> (and the rules <a class="internalDFN" href="#dfn-rdfs1">rdfs1</a> through <a class="internalDFN" href="#dfn-rdfs13">rdfs13</a>), with D={<code>rdf:langString</code>, <code>xsd:string</code>), to the set in all possible ways, to exhaustion. </p>
<p>Then we have the completeness result:</p>
-<p class="fact">If S is RDF (RDFS) consistent, then S RDF entails (RDFS entails) E just when the <a class="internalDFN" href="#dfn-generalized-rdf-rdfs-closure">generalized RDF (RDFS) closure</a> of S towards E simply entails E. </p>
+<p class="fact">If S is RDF (RDFS) consistent, then S RDF entails (RDFS entails) E just when the <a class="internalDFN" href="#dfn-generalized-rdf-rdfs-closure">generalized RDF (RDFS) closure</a> of S towards E simply entails E. </p>
<p>The closures are finite. The generation process is decidable and of polynomial complexity. Detecting simple entailment is NP-complete in general, but of low polynomial order when E contains no blank nodes. </p>
@@ -1336,9 +1376,10 @@
<p>As noted earlier, detecting datatype entailment for larger sets of datatype IRIs requires attention to idiosyncratic properties of the particular datatypes.</p>
</section>
-
-<section id="finite-interpretations-informative" rel="bibo:chapter" resource="#finite_interpretations" typeof="bibo:Chapter" class="informative appendix"><!--OddPage--><h2 id="finite_interpretations"><span class="secno">B. </span>Finite interpretations (Informative)</h2><p><em>This section is non-normative.</em></p>
-<p>To keep the exposition simple, the RDF semantics has been phrased in a way which requires interpretations to be larger than absolutely necessary. For example, all interpretations are required to interpret the whole IRI vocabulary, and the universes of all D-interpretations must contain all possible strings and therefore be infinite. This appendix sketches, without proof, how to re-state the semantics using smaller semantic structures, without changing any entailments. </p>
+
+<section id="finite-interpretations-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative appendix"><!--OddPage--><h2 role="heading" aria-level="1" id="finite_interpretations"><span class="secno">B. </span>Finite interpretations (Informative)</h2><p><em>This section is non-normative.</em></p>
+<p>To keep the exposition simple, the RDF semantics has been phrased in a way which requires interpretations to be larger than absolutely necessary. For example, all interpretations are required to interpret the whole IRI vocabulary, and the universes of all D-interpretations where D contains
+<code>xsd:string</code> must contain all possible strings and therefore be infinite. This appendix sketches, without proof, how to re-state the semantics using smaller semantic structures, without changing any entailments. </p>
<p>Basically, it is only necessary for an interpretation structure to interpret the <a class="internalDFN" href="#dfn-name">name</a>s actually used in the graphs whose entailment is being considered, and to consider interpretations whose universes are at most as big as the number of names and blank nodes in the graphs. More formally, we can define a <dfn id="dfn-pre-interpretation">pre-interpretation</dfn> over a <a class="internalDFN" href="#dfn-vocabulary">vocabulary</a> V to be a structure I similar to a <a class="internalDFN" href="#dfn-simple-interpretation">simple interpretation</a> but with a mapping only from V to its universe IR. Then when determining whether G entails E, consider only pre-interpretations over the finite vocabulary of <a class="internalDFN" href="#dfn-name">name</a>s actually used in G union E. The universe of such a pre-interpretation can be restricted to the cardinality N+B+1, where N is the size of the vocabulary and B is the number of blank nodes in the graphs. Any such pre-interpretation may be extended to <a class="internalDFN" href="#dfn-simple-interpretation">simple interpretation</a>s, all of which which will give the same truth values for any triples in G or E. Satisfiability, entailment and so on can then be defined with respect to these finite pre-interpretations, and shown to be identical to the ideas defined in the body of the specification.</p>
@@ -1349,41 +1390,41 @@
</p></section>
-<section id="proofs-of-some-results-informative" rel="bibo:chapter" resource="#proofs" typeof="bibo:Chapter" class="informative appendix"><!--OddPage--><h2 id="proofs"><span class="secno">C. </span>Proofs of some results (Informative)</h2><p><em>This section is non-normative.</em></p>
+<section id="proofs-of-some-results-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative appendix"><!--OddPage--><h2 role="heading" aria-level="1" id="proofs"><span class="secno">C. </span>Proofs of some results (Informative)</h2><p><em>This section is non-normative.</em></p>
-<p class="fact"> The <a class="internalDFN" href="#dfn-empty-graph">empty graph</a> is entailed by
- any graph, and does not entail any graph except itself.
+<p class="fact"> The <a class="internalDFN" href="#dfn-empty-graph">empty graph</a> is simply entailed by
+ any graph, and does not simply entail any graph except itself.
<!-- <a href="#emptygraphlemmaprf" class="termref">[Proof]</a> -->
</p>
-<p>The empty graph is true in all interpretations, so is entailed by any graph. If G contains a triple <a b c>, then any interpretation I with IEXT(I(b))={ } makes G false; so the empty graph does not entail G. QED.</p>
+<p>The empty graph is true in all simple interpretations, so is entailed by any graph. If G contains a triple <a b c>, then any simple interpretation I with IEXT(I(b))={ } makes G false; so the empty graph does not entail G. QED.</p>
-<p class="fact"> A graph entails all its subgraphs.
+<p class="fact"> A graph simply entails all its subgraphs.
<!-- <a href="#subglemprf" class="termref">[Proof]</a> -->
</p>
<p>If I satisfies G then it satisfies every triple in G, hence every triple in any subset of G. QED.</p>
-<p class="fact"> A graph
- is entailed by any of its <a class="internalDFN" href="#dfn-instance">instance</a>s.
+<p class="fact"> A graph
+ is simply entailed by any of its <a class="internalDFN" href="#dfn-instance">instance</a>s.
<!-- <a href="#instlemprf" class="termref"> [Proof]</a> -->
</p>
<p>Suppose H is an instance of G with the instantiation mapping M, and that I satisfies H. For blank nodes n in G which are not in H define A(n)=I(M(n)); then I+A satisfies G, so I satisfies G. QED.</p>
-<p class="fact">Every graph is satisfiable.</p>
+<p class="fact">Every graph is simply satisfiable.</p>
<p>Consider the simple interpretation with universe {x}, IEXT(x)= <x,x > and I(aaa)=x for any IRI aaa. This interpretation satisfies every RDF graph. QED.</p>
<p class="fact">
- G simply entails a graph E if and only if a subgraph of G is an instance of E.
+ G simply entails a graph E if and only if a subgraph of G is an instance of E.
</p>
-<p>If a subgraph E' of G is an instance of E then G entails E' which entails E, so G entails E. NOw suppose G entails E, and consider the <a>Herbrand interpretation</a> I of G defined as follows. IR contains the <a class="internalDFN" href="#dfn-name">name</a>s and blank nodes which occur in the graph, with I(n)=n for each <a class="internalDFN" href="#dfn-name">name</a> n; n is in IP and <a, b> in IEXT(n) just when the triple <a n b> is in the graph. (For IRIs which do not occur in the graph, assign them values in IR at random.) I satisfies every triple <s p o> in E; that is, for some mapping A from the blank nodes of E to the vocabulary of G, the triple <[I+A](s) I(p) [I+A](o)> occurs in G. But this is an instance of <s p o> under the instance mapping A; so an instance of E is a subgraph of G. QED.</p>
+<p>If a subgraph E' of G is an instance of E then G entails E' which entails E, so G entails E. Now suppose G entails E, and consider the <a href="http://en.wikipedia.org/wiki/Herbrand_interpretation">Herbrand interpretation</a> I of G defined as follows. IR contains the <a class="internalDFN" href="#dfn-name">name</a>s and blank nodes which occur in the graph, with I(n)=n for each <a class="internalDFN" href="#dfn-name">name</a> n; n is in IP and <a, b> in IEXT(n) just when the triple <a n b> is in the graph. (For IRIs which do not occur in the graph, assign them values in IR at random.) I satisfies every triple <s p o> in E; that is, for some mapping A from the blank nodes of E to the vocabulary of G, the triple <[I+A](s) I(p) [I+A](o)> occurs in G. But this is an instance of <s p o> under the instance mapping A; so an instance of E is a subgraph of G. QED.</p>
-<p class="fact">if E is lean and E' is a proper instance of E, then E does not entail E'.</p>
+<p class="fact">if E is lean and E' is a proper instance of E, then E does not simply entail E'.</p>
<p>Suppose E entails E', then a subgraph of E is an instance of E', which is a proper instance of E; so a subgraph of E is a proper instance of E, so E is not lean. QED.</p>
-<p class="fact">If E contains an IRI which does not occur in S, then S does not entail E.</p>
+<p class="fact">If E contains an IRI which does not occur in S, then S does not simply entail E.</p>
<p>IF S entails E then a subgraph of S is an instance of E, so every IRI in E must occur in that subgraph, so must occur in S. QED.</p>
-<p class="fact">For any graph H, if sk(G) entails H there there is a graph H' such that G entails H' and H=sk(H').</p>
+<p class="fact">For any graph H, if sk(G) simply entails H there there is a graph H' such that G entails H' and H=sk(H').</p>
<p>The skolemization mapping sk substitutes a unique new IRI for each blank node, so it is 1:1, so has an inverse. Define ks to be the inverse mapping which replaces each skolem IRI by the blank node it replaced. Since sk(G) entails H, a subgraph of sk(G) is an instance of H, say A(H) for some instance mapping A on the blank nodes in H. Then ks(A(H)) is a subgraph of G; and ks(A(H))=A(ks(H)) since the domains of A and ks are disjoint. So ks(H) has an instance which is a subgraph of G, so is entailed by G; and H=sk(ks(H)). QED.</p>
<p class="fact">For any graph H which does not contain any of the "new" IRIs introduced into sk(G), sk(G) simply entails H if and only if G simply entails H.</p>
@@ -1394,23 +1435,23 @@
</section>
-<section rel="bibo:chapter" resource="#whatnot" typeof="bibo:Chapter" class="informative appendix" id="whatnot"><!--OddPage--><h2 id="non_semantics"><span class="secno">D. </span>RDF reification, containers and collections (Informative)</h2><p><em>This section is non-normative.</em></p>
+<section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative appendix" id="whatnot"><!--OddPage--><h2 role="heading" aria-level="1" id="non_semantics"><span class="secno">D. </span>RDF reification, containers and collections (Informative)</h2><p><em>This section is non-normative.</em></p>
-<p>The RDF semantic conditions do not place formal constraints on the meaning
- of much of the RDF vocabulary which is intended for use in describing containers and bounded collections,
+<p>The RDF semantic conditions do not place formal constraints on the meaning
+ of much of the RDF vocabulary which is intended for use in describing containers and bounded collections,
or the reification vocabulary intended to enable an RDF graph to describe RDF triples. This appendix briefly reviews the intended meanings of this vocabulary. </p>
-<p>The omission of these conditions from the formal semantics is a design decision
- to accommodate variations in existing RDF usage and to make it easier to implement
- processes to check formal RDF entailment. For example, implementations may decide
+<p>The omission of these conditions from the formal semantics is a design decision
+ to accommodate variations in existing RDF usage and to make it easier to implement
+ processes to check formal RDF entailment. For example, implementations may decide
to use special procedural techniques to implement the RDF collection vocabulary.</p>
-<section id="reification" rel="bibo:chapter" resource="#Reif" typeof="bibo:Chapter">
-
-<h3 id="Reif"><span class="secno">D.1 </span>Reification</h3><p><em>This section is non-normative.</em></p>
+<section id="reification" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
- <div class="c1">
+<h3 role="heading" aria-level="2" id="Reif"><span class="secno">D.1 </span>Reification</h3>
+
+ <div class="c1">
<table border="1">
<tbody>
<tr>
@@ -1426,7 +1467,7 @@
<p>The intended meaning of this vocabulary is to allow an RDF graph to act as metadata describing other RDF triples. </p>
-
+
<p>Consider an example graph containing a single triple:</p>
<p><code>ex:a ex:b ex:c .</code></p>
@@ -1485,18 +1526,18 @@
<p><code>_:yyy ex:property ex:foo .</code></p>
</section>
-<section id="rdf-containers" rel="bibo:chapter" resource="#containers" typeof="bibo:Chapter">
-
-<h3 id="containers"><span class="secno">D.2 </span>RDF containers</h3>
+<section id="rdf-containers" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
+
+<h3 role="heading" aria-level="2" id="containers"><span class="secno">D.2 </span>RDF containers</h3>
<table border="1">
<tbody>
<tr>
- <td class="othertable"><strong>RDF Container Vocabulary</strong></td>
+ <td class="othertable"><strong>RDF(S) Container Vocabulary</strong></td>
</tr>
<tr>
<td class="othertable"><code>rdf:Seq rdf:Bag rdf:Alt rdf:_1 rdf:_2
- ...</code></td>
+ ... rdfs:member rdfs:Container rdfs:ContainerMembershipProperty</code></td>
</tr>
</tbody>
</table>
@@ -1538,11 +1579,11 @@
If the container is of an ordered type, then the ordering of items in the container is intended to be
indicated by the numerical ordering of the container membership
properties, which are assumed to be single-valued.
- However, these informal interpretations are not reflected in any formal RDF
+ However, these informal conditions are not reflected in any formal RDF
entailments.</p>
-
-<p>The RDF semantics does not support any entailments which could arise from enumerating
+
+<p>The RDF semantics does not support any entailments which could arise from enumerating
the elements of an unordered <code>rdf:Bag</code> in a different order. For example,</p>
<p><code>_:xxx rdf:type rdf:Bag .<br>
@@ -1555,7 +1596,7 @@
_:xxx rdf:_2 ex:a .</code></p>
<p>(If this conclusion were <a class="internalDFN" href="#dfn-valid">valid</a>, then the result of
- adding it to the original graph would be <a>entailed</a> by the graph, and this would assert that both elements were in both
+ adding it to the original graph would be <a class="internalDFN" href="#dfn-entail">entail</a>ed by the graph, and this would assert that both elements were in both
positions. This is a consequence of the fact that RDF is a purely
assertional language.)</p>
@@ -1563,7 +1604,7 @@
any of the elements of the container, or vice versa. </p>
<p>There is no formal requirement that
the three container classes are disjoint, so that for example
- it is consistent to assert that something is both an <code>rdf:Bag</code> and an <code>rdf:Seq</code>.
+ it is consistent to assert that something is both an <code>rdf:Bag</code> and an <code>rdf:Seq</code>.
There is no assumption that containers are gap-free, so that for example</p>
<p><code>_:xxx rdf:type rdf:Seq.<br>
_:xxx rdf:_1 ex:a .<br>
@@ -1581,9 +1622,9 @@
only finitely many members.</p>
</section>
-<section id="rdf-collections" rel="bibo:chapter" resource="#collections" typeof="bibo:Chapter">
-
-<h3 id="collections"><span class="secno">D.3 </span>RDF collections</h3>
+<section id="rdf-collections" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter">
+
+<h3 role="heading" aria-level="2" id="collections"><span class="secno">D.3 </span>RDF collections</h3>
<table border="1">
<tbody>
@@ -1601,26 +1642,26 @@
explicit terminator, allowing applications to determine the exact
set of items in the collection.</p>
-
-<p>As with containers, no special semantic conditions are imposed on this vocabulary
- other than the type of <code>rdf:nil</code> being <code>rdf:List</code>. It
- is intended for use typically in a context where a container is described using
- blank nodes to connect a 'well-formed' sequence of items, each described by
+
+<p>As with containers, no special semantic conditions are imposed on this vocabulary
+ other than the type of <code>rdf:nil</code> being <code>rdf:List</code>. It
+ is intended for use typically in a context where a container is described using
+ blank nodes to connect a 'well-formed' sequence of items, each described by
two triples of the form
<code><br>
<br>
_:c1 rdf:first aaa .<br>
_:c1 rdf:rest _:c2 .</code></p>
-
-<p>where the final item is indicated by the use of <code>rdf:nil</code> as the
- value of the property <code>rdf:rest</code>. In a familiar convention, <code>rdf:nil</code>
- can be thought of as the empty collection. Any such graph amounts to an assertion
- that the collection exists, and since the members of the collection can be determined
- by inspection, this is often sufficient to enable applications to determine
- what is meant. The semantics does not require any collections
- to exist other than those mentioned explicitly in a graph (and the empty collection).
- For example, the existence of a collection containing two items does not automatically
+
+<p>where the final item is indicated by the use of <code>rdf:nil</code> as the
+ value of the property <code>rdf:rest</code>. In a familiar convention, <code>rdf:nil</code>
+ can be thought of as the empty collection. Any such graph amounts to an assertion
+ that the collection exists, and since the members of the collection can be determined
+ by inspection, this is often sufficient to enable applications to determine
+ what is meant. The semantics does not require any collections
+ to exist other than those mentioned explicitly in a graph (and the empty collection).
+ For example, the existence of a collection containing two items does not automatically
guarantee that the similar collection with the items permuted also exists:
<code>
<br><br>
@@ -1629,7 +1670,7 @@
_:c2 rdf:first ex:bbb .<br>
_:c2 rdf:rest rdf:nil . </code></p>
<p>does not entail</p>
-
+
<p><code>_:c3 rdf:first ex:bbb .<br>
_:c3 rdf:rest _:c4 .<br>
<span>_:c4 rdf:first</span> ex:aaa .<br>
@@ -1640,62 +1681,83 @@
vocabulary, so that it is possible to write RDF graphs which assert
the existence of highly peculiar objects such as lists with forked
or non-list tails, or multiple heads:</p>
-
+
<p><code>_:666 rdf:first ex:aaa .<br>
_:666 rdf:first ex:bbb .<br>
_:666 rdf:rest ex:ccc .<br>
_:666 rdf:rest rdf:nil . </code></p>
-
-<p>It is also possible to write a set of triples which under-specify a collection
+
+<p>It is also possible to write a set of triples which under-specify a collection
by failing to specify its <code>rdf:rest</code> property value.</p>
-
+
<p><a class="internalDFN" href="#dfn-semantic-extension">Semantic extension</a>s may
- place extra syntactic well-formedness restrictions on the use of this vocabulary
+ place extra syntactic well-formedness restrictions on the use of this vocabulary
in order to rule out such graphs. They may
- exclude interpretations of the collection vocabulary which violate the convention
- that the subject of a 'linked' collection of two-triple items of the form described
- above, ending with an item ending with <code>rdf:nil</code>, denotes a totally
- ordered sequence whose members are the denotations of the <code>rdf:first</code>
- values of the items, in the order got by tracing the <code>rdf:rest</code> properties
- from the subject to <code>rdf:nil</code>. This permits sequences which contain
+ exclude interpretations of the collection vocabulary which violate the convention
+ that the subject of a 'linked' collection of two-triple items of the form described
+ above, ending with an item ending with <code>rdf:nil</code>, denotes a totally
+ ordered sequence whose members are the denotations of the <code>rdf:first</code>
+ values of the items, in the order got by tracing the <code>rdf:rest</code> properties
+ from the subject to <code>rdf:nil</code>. This permits sequences which contain
other sequences.</p>
-<p> The RDFS semantic conditions require that any
- subject of the <code>rdf:first</code> property, and any subject or object of
+<p> The RDFS semantic conditions require that any
+ subject of the <code>rdf:first</code> property, and any subject or object of
the <code>rdf:rest</code> property, be of <code>rdf:type rdf:List</code>. </p>
</section>
</section>
- <section id="acknowledgements-1" rel="bibo:chapter" resource="#acknowledgements" typeof="bibo:Chapter" class="informative appendix">
- <!--OddPage--><h2 id="acknowledgements"><span class="secno">E. </span>Acknowledgements</h2><p><em>This section is non-normative.</em></p>
+ <section id="change-log-informative" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative appendix">
+ <!--OddPage--><h2 role="heading" aria-level="1" id="ChangeLog"><span class="secno">E. </span>Change Log (informative)</h2><p><em>This section is non-normative.</em></p>
+<p>Changes since Last Call:</p>
+<ul>
+<li> Repaired several broken internal links and typos.</li>
+<li> Added table of RDF vocabulary. </li>
+<li> Added text mentioning lexical spaces in datatypes.</li>
+<li> Added extended change note defining datatype map.</li>
+<li> Removed informative section on intuitive summary of truth conditions </li>
+<li> Added a general description of the notion of interpretation. </li>
+<li> Adjusted several uses of "interpretation" and related terminology to state the particular kind of interpretation in question or use a more appropriate term. </li>
+<li> Brian McBride was acknowledged as series editor of the previous
+ version. </li>
+<li> The wording looking like a definition of RDF Datasets was replaced by
+ more informative wording. </li>
+<li> This change log was added. </li>
+</ul>
+</section>
+
+
+ <section id="acknowledgements-1" rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" class="informative appendix">
+ <!--OddPage--><h2 role="heading" aria-level="1" id="acknowledgements"><span class="secno">F. </span>Acknowledgements</h2><p><em>This section is non-normative.</em></p>
<p>The basic idea of using an explicit extension mapping to allow self-application without violating the axiom of foundation was
suggested by Christopher Menzel. The generalized RDF syntax used in Appendix A, and the example showing the need for it, were suggested by Herman ter Horst, who also proved completeness and complexity results for the rule sets. Jeremy Carroll first showed that simple entailment is NP-complete in general. Antoine Zimmerman suggested several simplifications and improvements to the proofs and presentation.</p>
<p>The RDF 1.1 editors acknowledge valuable contributions from Thomas Baker, Dan Brickley, Gavin Carothers, Jeremy Carroll, Pierre-Antoine Champin, Richard Cyganiak, Martin J. Dürst, Alex Hall, Steve Harris, Ivan Herman, Eric Prud'hommeaux, Andy Seaborne, David Wood and Antoine Zimmermann. </p>
-<p>This specification is a product of extended deliberations by <a href="http://www.w3.org/2000/09/dbwg/details?group=46168&public=1">members of the RDF Working Group</a>. It draws upon the earlier specification [<cite><a href="#bib-RDF-MT" class="bibref">RDF-MT</a></cite>], whose editor acknowledged valuable inputs from Jeremy Carroll, Dan Connolly, Jan Grant, R. V. Guha, Herman ter Horst, Graham Klyne, Ora Lassilla, Brian McBride, Sergey Melnick, Peter Patel-Schneider, Jos deRoo and Patrick Stickler.
-
+<p>This specification is a product of extended deliberations by <a href="http://www.w3.org/2000/09/dbwg/details?group=46168&public=1">members of the RDF Working Group</a>. This specification draws upon the earlier specification [<cite><a href="#bib-RDF-MT" class="bibref">RDF-MT</a></cite>], whose editor acknowledged valuable inputs from Jeremy Carroll, Dan Connolly, Jan Grant, R. V. Guha, Herman ter Horst, Graham Klyne, Ora Lassilla, Brian McBride, Sergey Melnick, Peter Patel-Schneider, Jos deRoo and Patrick Stickler.
+Brian McBride was the series editor for this earlier specification.
</p>
<p>This document was prepared using the <a href="http://dev.w3.org/2009/dap/ReSpec.js/documentation.html">ReSpec.js specification writing tool</a> developed by Robin Berjon. </p>
-
+
</section>
-<section rel="bibo:chapter" resource="#references" typeof="bibo:Chapter" class="appendix" id="references"><!--OddPage--><h2><span class="secno">F. </span>References</h2><section rel="bibo:chapter" resource="#normative-references" typeof="bibo:Chapter" id="normative-references"><h3><span class="secno">F.1 </span>Normative references</h3><dl about="" class="bibliography"><dt id="bib-OWL2-SYNTAX">[OWL2-SYNTAX]</dt><dd rel="dcterms:requires">Boris Motik; Peter Patel-Schneider; Bijan Parsia. <a href="http://www.w3.org/TR/owl2-syntax/"><cite>OWL 2 Web Ontology Language Structural Specification and Functional-Style Syntax (Second Edition)</cite></a>. 11 December 2012. W3C Recommendation. URL: <a href="http://www.w3.org/TR/owl2-syntax/">http://www.w3.org/TR/owl2-syntax/</a>
-</dd><dt id="bib-RDF-PLAIN-LITERAL">[RDF-PLAIN-LITERAL]</dt><dd rel="dcterms:requires">Jie Bao, Sandro Hawke, Boris Motik, Peter F. Patel-Schneider, Alex Polleres. <cite><a href="http://www.w3.org/TR/rdf-plain-literal/">rdf:PlainLiteral: A Datatype for RDF Plain Literals (Second Edition)</a></cite> 11 December 2012. W3C Recommendation. URL: <a href="http://www.w3.org/TR/rdf-plain-literal/">http://www.w3.org/TR/rdf-plain-literal/</a>
-</dd><dt id="bib-RDF11-CONCEPTS">[RDF11-CONCEPTS]</dt><dd rel="dcterms:requires">Richard Cyganiak, David Wood. <cite><a href="http://www.w3.org/TR/2013/WD-rdf11-concepts-20130723/">RDF 1.1 Concepts and Abstract Syntax.</a></cite> 23 July 2013. W3C Last Call Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-rdf11-concepts-20130723/">http://www.w3.org/TR/2013/WD-rdf11-concepts-20130723/</a>. The latest edition is available at <a href="http://www.w3.org/TR/rdf11-concepts/">http://www.w3.org/TR/rdf11-concepts/</a>
+<section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" id="references" class="appendix"><!--OddPage--><h2 id="h2_references" role="heading" aria-level="1"><span class="secno">G. </span>References</h2><section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" id="normative-references"><h3 id="h3_normative-references" role="heading" aria-level="2"><span class="secno">G.1 </span>Normative references</h3><dl about="" class="bibliography"><dt id="bib-RDF-PLAIN-LITERAL">[RDF-PLAIN-LITERAL]</dt><dd rel="dcterms:requires">Jie Bao, Sandro Hawke, Boris Motik, Peter F. Patel-Schneider, Alex Polleres. <cite><a href="http://www.w3.org/TR/rdf-plain-literal/">rdf:PlainLiteral: A Datatype for RDF Plain Literals (Second Edition)</a></cite> 11 December 2012. W3C Recommendation. URL: <a href="http://www.w3.org/TR/rdf-plain-literal/">http://www.w3.org/TR/rdf-plain-literal/</a>
+</dd><dt id="bib-RDF11-CONCEPTS">[RDF11-CONCEPTS]</dt><dd rel="dcterms:requires">Richard Cyganiak, David Wood, Markus Lanthaler, Editors. <cite><a href="http://www.w3.org/TR/2013/CR-rdf11-concepts-20131105/">RDF 1.1 Concepts and Abstract Syntax.</a></cite> 5 November 2013. W3C Candidate Recommendation (work in progress). URL: <a href="http://www.w3.org/TR/2013/CR-rdf11-concepts-20131105/">http://www.w3.org/TR/2013/CR-rdf11-concepts-20131105/</a>. The latest edition is available at <a href="http://www.w3.org/TR/rdf11-concepts/">http://www.w3.org/TR/rdf11-concepts/</a>
</dd><dt id="bib-RFC2119">[RFC2119]</dt><dd rel="dcterms:requires">S. Bradner. <a href="http://www.ietf.org/rfc/rfc2119.txt"><cite>Key words for use in RFCs to Indicate Requirement Levels.</cite></a> March 1997. Internet RFC 2119. URL: <a href="http://www.ietf.org/rfc/rfc2119.txt">http://www.ietf.org/rfc/rfc2119.txt</a>
-</dd><dt id="bib-TURTLE-CR">[TURTLE-CR]</dt><dd rel="dcterms:requires">Eric Prud'hommeaux, Gavin Carothers. <cite><a href="http://www.w3.org/TR/2013/CR-turtle-20130219/">Turtle; Terse RDF Triple Language</a></cite>. 19 February 2013. W3C Candidate Recommendation. URL: <a href="http://www.w3.org/TR/2013/CR-turtle-20130219/">http://www.w3.org/TR/2013/CR-turtle-20130219/</a>. The latest edition is available at <a href="http://www.w3.org/TR/turtle/">http://www.w3.org/TR/turtle/</a>
-</dd></dl></section><section rel="bibo:chapter" resource="#informative-references" typeof="bibo:Chapter" id="informative-references"><h3><span class="secno">F.2 </span>Informative references</h3><dl about="" class="bibliography"><dt id="bib-HORST04">[HORST04]</dt><dd rel="dcterms:references">Herman J. ter Horst. <cite>Extending the RDFS Entailment Lemma</cite>, in S.A. McIlraith et al. (Eds.), The Semantic Web - ISWC2004, Proceedings of the Third International Semantic Web Conference, Hiroshima, Japan, November 2004, Springer, LNCS 3298, pp. 77-91.
+</dd><dt id="bib-SPARQL11-ENTAILMENT">[SPARQL11-ENTAILMENT]</dt><dd rel="dcterms:requires">Birte Glimm; Chimezie Ogbuji. <a href="http://www.w3.org/TR/sparql11-entailment/"><cite>SPARQL 1.1 Entailment Regimes</cite></a>. 21 March 2013. W3C Recommendation. URL: <a href="http://www.w3.org/TR/sparql11-entailment/">http://www.w3.org/TR/sparql11-entailment/</a>
+</dd><dt id="bib-TURTLE">[TURTLE]</dt><dd rel="dcterms:requires">Eric Prud'hommeaux, Gavin Carothers, Editors. <cite><a href="http://www.w3.org/TR/2013/CR-turtle-20130219/">RDF 1.1 Turtle: Terse RDF Triple Language.</a></cite> 19 February 2013. W3C Candidate Recommendation (work in progress). URL: <a href="http://www.w3.org/TR/2013/CR-turtle-20130219/">http://www.w3.org/TR/2013/CR-turtle-20130219/</a>. The latest edition is available at <a href="http://www.w3.org/TR/turtle/">http://www.w3.org/TR/turtle/</a>
+</dd></dl></section><section rel="bibo:Chapter" resource="#ref" typeof="bibo:Chapter" id="informative-references"><h3 id="h3_informative-references" role="heading" aria-level="2"><span class="secno">G.2 </span>Informative references</h3><dl about="" class="bibliography"><dt id="bib-HORST04">[HORST04]</dt><dd rel="dcterms:references">Herman J. ter Horst. <cite>Extending the RDFS Entailment Lemma</cite>, in S.A. McIlraith et al. (Eds.), The Semantic Web - ISWC2004, Proceedings of the Third International Semantic Web Conference, Hiroshima, Japan, November 2004, Springer, LNCS 3298, pp. 77-91.
</dd><dt id="bib-HORST05">[HORST05]</dt><dd rel="dcterms:references">Herman J. ter Horst. <cite>Completeness, Decidability and Complexity of Entailment for RDF Schema and a Semantic Extension Involving the OWL Vocabulary</cite>, Journal of Web Semantics 3 (2005) 79-115.
</dd><dt id="bib-ISO24707">[ISO24707]</dt><dd rel="dcterms:references"><cite>Information technology — Common Logic (CL): a framework for a family of logic-based languages</cite> 1 October 2007. International Standard ISO/IEC 24707:2007(E). URL: <a href="http://standards.iso.org/ittf/PubliclyAvailableStandards/c039175_ISO_IEC_24707_2007%28E%29.zip"> http://standards.iso.org/ittf/PubliclyAvailableStandards/c039175_ISO_IEC_24707_2007%28E%29.zip</a>
</dd><dt id="bib-OWL2-OVERVIEW">[OWL2-OVERVIEW]</dt><dd rel="dcterms:references">W3C OWL Working Group. <a href="http://www.w3.org/TR/owl2-overview/"><cite>OWL 2 Web Ontology Language Document Overview (Second Edition)</cite></a>. 11 December 2012. W3C Recommendation. URL: <a href="http://www.w3.org/TR/owl2-overview/">http://www.w3.org/TR/owl2-overview/</a>
</dd><dt id="bib-OWL2-PROFILES">[OWL2-PROFILES]</dt><dd rel="dcterms:references">Boris Motik; Bernardo Cuenca Grau; Ian Horrocks; Zhe Wu; Achille Fokoue. <a href="http://www.w3.org/TR/owl2-profiles/"><cite>OWL 2 Web Ontology Language Profiles (Second Edition)</cite></a>. 11 December 2012. W3C Recommendation. URL: <a href="http://www.w3.org/TR/owl2-profiles/">http://www.w3.org/TR/owl2-profiles/</a>
+</dd><dt id="bib-OWL2-SYNTAX">[OWL2-SYNTAX]</dt><dd rel="dcterms:references">Boris Motik; Peter Patel-Schneider; Bijan Parsia. <a href="http://www.w3.org/TR/owl2-syntax/"><cite>OWL 2 Web Ontology Language Structural Specification and Functional-Style Syntax (Second Edition)</cite></a>. 11 December 2012. W3C Recommendation. URL: <a href="http://www.w3.org/TR/owl2-syntax/">http://www.w3.org/TR/owl2-syntax/</a>
</dd><dt id="bib-RDF-MT">[RDF-MT]</dt><dd rel="dcterms:references">Patrick Hayes. <a href="http://www.w3.org/TR/rdf-mt/"><cite>RDF Semantics</cite></a>. 10 February 2004. W3C Recommendation. URL: <a href="http://www.w3.org/TR/rdf-mt/">http://www.w3.org/TR/rdf-mt/</a>
</dd><dt id="bib-RDF-SCHEMA">[RDF-SCHEMA]</dt><dd rel="dcterms:references">Dan Brickley; Ramanathan Guha. <a href="http://www.w3.org/TR/rdf-schema"><cite>RDF Vocabulary Description Language 1.0: RDF Schema</cite></a>. 10 February 2004. W3C Recommendation. URL: <a href="http://www.w3.org/TR/rdf-schema">http://www.w3.org/TR/rdf-schema</a>
</dd><dt id="bib-RDF-SPARQL-QUERY">[RDF-SPARQL-QUERY]</dt><dd rel="dcterms:references">Eric Prud'hommeaux; Andy Seaborne. <a href="http://www.w3.org/TR/rdf-sparql-query/"><cite>SPARQL Query Language for RDF</cite></a>. 15 January 2008. W3C Recommendation. URL: <a href="http://www.w3.org/TR/rdf-sparql-query/">http://www.w3.org/TR/rdf-sparql-query/</a>