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-</style><link href="https://www.w3.org/StyleSheets/TR/W3C-WD" rel="stylesheet" type="text/css" charset="utf-8" /></head>
- <body style="display: inherit;"><div class="head"><p><a href="http://www.w3.org/"><img width="72" height="48" alt="W3C" src="http://www.w3.org/Icons/w3c_home" /></a></p><h1 id="title" class="title">RDF 1.1 Semantics</h1><h2 id="w3c-working-draft-02-april-2013"><acronym title="World Wide Web Consortium">W3C</acronym> Working Draft 02 April 2013</h2><dl><dt>This version:</dt><dd><a href="http://www.w3.org/TR/2013/WD-rdf11-mt-20130402/">http://www.w3.org/TR/2013/WD-rdf11-mt-20130402/</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><dt>Latest editor's draft:</dt><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>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><a href="http://www.ihmc.us/groups/phayes/">Patrick J. Hayes</a>, <a href="http://www.ihmc.us/index.php">Florida IHMC</a></dd>
-<dd><span>Peter F. Patel-Schneider</span>, <a href="http://www.nuance.com/">Nuance Communications</a></dd>
-</dl><p class="copyright"><a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> © 2004-2013 <a href="http://www.w3.org/"><acronym title="World Wide Web Consortium">W3C</acronym></a><sup>®</sup> (<a href="http://www.csail.mit.edu/"><acronym title="Massachusetts Institute of Technology">MIT</acronym></a>, <a href="http://www.ercim.eu/"><acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym></a>, <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved. <acronym title="World Wide Web Consortium">W3C</acronym> <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.</p><hr /></div>
- <div id="abstract" class="introductory section"><h2>Abstract</h2>
- <p> This document describes a precise semantics for the Resource Description
- Framework 1.1 [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF-PRIMER">RDF-PRIMER</a></cite>] and RDF Schema [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF-SCHEMA">RDF-SCHEMA</a></cite>]. It defines a number of distinct entailment regimes and corresponding systems of inference rules. It is part of a suite of documents which comprise the full specification of RDF 1.1.</p>
-<p>This is a revision of the 2004 RDF Semantics specification for RDF
- [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF-MT">RDF-MT</a></cite>] and supersedes that document. </p> </div><div class="introductory section" id="sotd"><h2>Status of This Document</h2><p><em>This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current <acronym title="World Wide Web Consortium">W3C</acronym> publications and the latest revision of this technical report can be found in the <a href="http://www.w3.org/TR/"><acronym title="World Wide Web Consortium">W3C</acronym> technical reports index</a> at http://www.w3.org/TR/.</em></p>
-<p>This is a revision of the 2004 Semantics specification for RDF
- [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF-MT">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 First Public Working Draft. This document is intended to become a <acronym title="World Wide Web Consortium">W3C</acronym> Recommendation. If you wish to make comments regarding this document, please send them to <a href="mailto:public-rdf-comments@w3.org">public-rdf-comments@w3.org</a> (<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>). All feedback is welcome.</p><p>Publication as a Working Draft does not imply endorsement by the <acronym title="World Wide Web Consortium">W3C</acronym> 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 document was produced by a group operating under the <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/">5 February 2004 <acronym title="World Wide Web Consortium">W3C</acronym> Patent Policy</a>. <acronym title="World Wide Web Consortium">W3C</acronym> maintains a <a rel="disclosure" href="http://www.w3.org/2004/01/pp-impl/46168/status">public list of any patent disclosures</a> made in connection with the deliverables of the group; that page also includes instructions for disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential Claim(s)</a> must disclose the information in accordance with <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section 6 of the <acronym title="World Wide Web Consortium">W3C</acronym> Patent Policy</a>.</p></div><div id="toc" class="section"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a href="#introduction" class="tocxref"><span class="secno">1 </span>Introduction</a></li><li class="tocline"><a href="#semantic-extensions-and-entailment-regimes" class="tocxref"><span class="secno">2 </span>Semantic extensions and entailment regimes</a></li><li class="tocline"><a href="#notation-and-terminology" class="tocxref"><span class="secno">3 </span>Notation and terminology</a></li><li class="tocline"><a href="#simple-interpretations" class="tocxref"><span class="secno">4 </span> Simple Interpretations</a></li><li class="tocline"><a href="#simple-entailment" class="tocxref"><span class="secno">5 </span>Simple Entailment</a></li><li class="tocline"><a href="#skolemization" class="tocxref"><span class="secno">6 </span>Skolemization</a></li><li class="tocline"><a href="#literals-and-datatypes" class="tocxref"><span class="secno">7 </span>Literals and datatypes</a></li><li class="tocline"><a href="#d-interpretations-and-datatype-entailment" class="tocxref"><span class="secno">8 </span>D-interpretations and datatype entailment</a></li><li class="tocline"><a href="#rdf-d-interpretations-and-rdf-entailment" class="tocxref"><span class="secno">9 </span>RDF-D Interpretations and RDF entailment</a></li><li class="tocline"><a href="#rdfs-interpretations-and-rdfs-entailment" class="tocxref"><span class="secno">10 </span>RDFS Interpretations and RDFS entailment</a></li><li class="tocline"><a href="#monotonicity-of-semantic-extensions" class="tocxref"><span class="secno">11 </span>Monotonicity of semantic extensions </a></li><li class="tocline"><a href="#extensional-rdfs-semantic-conditions--informative" class="tocxref"><span class="secno">12 </span>Extensional RDFS Semantic Conditions (Informative)</a></li><li class="tocline"><a href="#entailment-rules--informative" class="tocxref"><span class="secno">13 </span>Entailment Rules (Informative)</a></li><li class="tocline"><a href="#MTintro" class="tocxref"><span class="secno">A </span>Introduction to model theory (Informative)</a></li><li class="tocline"><a href="#proofs" class="tocxref"><span class="secno">B </span>Proofs of Lemmas (Informative)</a></li><li class="tocline"><a href="#whatnot" class="tocxref"><span class="secno">C </span>What the semantics does not do (Informative)</a></li><li class="tocline"><a href="#glossary" class="tocxref"><span class="secno">D </span>Glossary of Terms (Informative)</a></li><li class="tocline"><a href="#acknowledgements" class="tocxref"><span class="secno">E </span>Acknowledgements</a></li><li class="tocline"><a href="#references" class="tocxref"><span class="secno">F </span>References</a><ul class="toc"><li class="tocline"><a href="#normative-references" class="tocxref"><span class="secno">F.1 </span>Normative references</a></li><li class="tocline"><a href="#informative-references" class="tocxref"><span class="secno">F.2 </span>Informative references</a></li></ul></li></ul></div>
-
-
-
- <div class="introductory section"><h2 id="notes">Notes</h2>
-<p class="changenote">Notes in this style indicate changes from the 2004 RDF semantics.</p>
-<p class="technote">Notes in this style are technical asides on obscure or recondite matters.</p></div>
- <div id="introduction" class="section">
- <h2><span class="secno">1 </span>Introduction</h2>
+ <section class='introductory'><h2 id="notes">Notes</h2>
+<p class='changenote'>Notes in this style indicate changes from the 2004 RDF semantics.</p>
+<p class='technote'>Notes in this style are technical asides on obscure or recondite matters.</p></section>
+ <section>
+ <h2 id="introduction">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. Readers who are unfamiliar with model theory can find a brief introduction to the basic ideas and terminology in <a>Appendix A</a>, and may find the informative section 13 useful. </p>
-<p>This specification is normative for RDF <a>formal</a> semantics. However, there are many aspects of RDF meaning which are not covered 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. Accounts of such extended notions of meaning will go beyond this specification, but <em class="rfc2119" title="must not">must not</em> violate the conditions described here. </p>
- </div>
+<p>This specification is normative for RDF <a>formal</a> semantics. However, there are many aspects of RDF meaning which are not covered 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. Accounts of such extended notions of meaning will go beyond this specification, but MUST NOT violate the conditions described here. </p>
+ </section>
- <div id="semantic-extensions-and-entailment-regimes" class="section">
- <h2><span class="secno">2 </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 class="bibref" rel="biblioentry" href="#bib-OWL2-OVERVIEW">OWL2-OVERVIEW</a></cite>] and RIF [<cite><a class="bibref" rel="biblioentry" href="#bib-RIF-OVERVIEW">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 impose user-defined meanings upon the basic RDF meaning rules. 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 valid entailments it has. </p>
-
-<p>A particular such set of semantic assumptions is called a <dfn id="dfn-semantic-extension">semantic extension</dfn>. Each semantic extension 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 semantic extension. We will refer to an entailment regime by names such as <em>rdfs-entailment</em>, <em>D-entailment</em>, etc.. </p>
+ <section>
+ <h2 id="extensions">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 [[OWL2-OVERVIEW]] and RIF [[RIF-OVERVIEW]], whose expressions can be encoded as RDF graphs which use a particular vocabulary with a specially defined meaning. Also, particular IRI vocabularies may impose user-defined meanings upon the basic RDF meaning rules. 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 valid entailments it has. </p>
-<p>Semantic extensions <em class="rfc2119" title="may">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 class="rfc2119" title="may">may</em> consider RDF graphs which do not conform to these conditions to be errors. For example, RDF statements of the form <br />
-<code>:a rdfs:subClassOf owl:Thing .</code><br />
-are prohibited in the OWL-DL [<cite><a class="bibref" rel="biblioentry" href="#bib-OWL2-SYNTAX">OWL2-SYNTAX</a></cite>] semantic extension. In such cases, basic RDF operations such as taking a subset of triples, or merging RDF graphs, may cause syntax errors in parsers which recognize the extension conditions. None of the semantic extensions normatively defined in this document impose syntactic restrictions on RDF graphs.</p>
+<p>A particular such set of semantic assumptions is called a <dfn>semantic extension</dfn>. Each semantic extension defines an <dfn>entailment regime</dfn> of entailments which are valid under that extension. RDFS, described later in this document, is one such semantic extension. We will refer to an entailment regime by names such as <em>rdfs-entailment</em>, <em>D-entailment</em>, etc.. </p>
-<p>All entailment regimes <em class="rfc2119" title="must">must</em> be <a>monotonic</a> extensions of the simple entailment regime described in the next section, in the sense that if A simply entails B then A also entails B under any extended notion of entailment, provided of course that any syntactic conditions of the extension are also satisfied. Put another way, a semantic extension cannot "cancel" an entailment made by a weaker entailment regime, although it can treat the result as a syntax error.</p>
- </div>
+<p>Semantic extensions MAY 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 MAY consider RDF graphs which do not conform to these conditions to be errors. For example, RDF statements of the form <br/>
+<code>:a rdfs:subClassOf owl:Thing .</code><br/>
+are prohibited in the OWL-DL [[OWL2-SYNTAX]] semantic extension. In such cases, basic RDF operations such as taking a subset of triples, or merging RDF graphs, may cause syntax errors in parsers which recognize the extension conditions. None of the semantic extensions normatively defined in this document impose syntactic restrictions on RDF graphs.</p>
- <div id="notation-and-terminology" class="section">
- <h2><span class="secno">3 </span>Notation and terminology</h2>
+<p>All entailment regimes MUST be <a>monotonic</a> extensions of the simple entailment regime described in the next section, in the sense that if A simply entails B then A also entails B under any extended notion of entailment, provided of course that any syntactic conditions of the extension are also satisfied. Put another way, a semantic extension cannot "cancel" an entailment made by a weaker entailment regime, although it can treat the result as a syntax error.</p>
+ </section>
-<p class="issue">This section needs cleaning up. Some of the 2004 definitions may no longer be needed. The notions of instance and equivalence may (?) need to be stated more carefully taking bnode scopes into account. Instance mappings should be defined on a whole scope rather than a graph (?). The definitions involving bnode scopes and complete graphs are new. <br /><br /> Maybe some of the material should be in Concepts. </p>
+ <section>
+ <h2 id="notation">Notation and terminology</h2>
+
+<p class="issue">This section needs cleaning up. Some of the 2004 definitions may no longer be needed. The notions of instance and equivalence may (?) need to be stated more carefully taking bnode scopes into account. Instance mappings should be defined on a whole scope rather than a graph (?). The definitions involving bnode scopes and complete graphs are new. <br/><br/> Maybe some of the material should be in Concepts. </p>
<p>This document uses the terminology //list terms// defined in //Concepts// for describing RDF graph syntax.</p>
<p>Throughout this document, precise semantic conditions will be set out in tables
- which state semantic conditions, tables containing true assertions and <a href="#dfn-valid" class="internalDFN">valid</a> inference rules, and tables listing syntax. These tables, which
+ which state semantic conditions, tables containing true assertions and <a>valid</a> inference rules, and tables listing syntax. These tables, which
are distinguished by background color, amount
to a formal summary of the entire semantics.
</p>
<p>Throughout this document, the equality sign = indicates
- identity. The statement "A = B" means that there is one entity which both expressions "A" and "B" refer to. Angle brackets < x, y > are used to indicate an ordered pair
+ identity. The statement "A = B" means that there is one entity which both expressions "A" and "B" refer to. Angle brackets < x, y > are used to indicate an ordered pair
of x and y. RDF graph syntax is indicated using the notational conventions of
the N-Triples syntax described
- in the <a href="https://dvcs.w3.org/hg/rdf/raw-file/default/rdf-turtle/n-triples.html">Turtle Working Draft</a> [<cite><a class="bibref" rel="biblioentry" href="#bib-TURTLE">TURTLE</a></cite>]
+ in the <a
+ href="https://dvcs.w3.org/hg/rdf/raw-file/default/rdf-turtle/n-triples.html">Turtle Working Draft</a> [[TURTLE]]
literal strings are enclosed within double quote marks and attached to a type IRI using a double-caret <code>^^</code>, language tags indicated
by the use of the <code>@</code> sign, and triples terminate with a 'code dot'
<code>.</code> . </p>
-<p>In stating general rules or conditions we will use the following conventions:<br />
-sss or ttt indicates a Unicode character string; <br />
-aaa or bbb indicates an IRI<br />
-lll or mmm indicates a literal<br />
-_:xxx or _:yyy indicates a blank node. <br /></p>
+<p>In stating general rules or conditions we will use the following conventions:<br/>
+sss or ttt indicates a Unicode character string; <br/>
+aaa or bbb indicates an IRI<br/>
+lll or mmm indicates a literal<br/>
+_:xxx or _:yyy indicates a blank node. <br/></p>
-<p>A <dfn id="dfn-name">name</dfn> is any IRI or literal. A <dfn id="dfn-vocabulary">vocabulary</dfn> is a set of names.
+<p>A <dfn>name</dfn> is any IRI or literal. A <dfn>vocabulary</dfn> is a set of names.
</p>
<p>An <a class="externalDFN">RDF
- graph</a>, or simply a <dfn id="dfn-graph">graph</dfn>, is a set of RDF triples.</p>
-<p>A <dfn id="dfn-subgraph">subgraph</dfn> of an RDF graph is a subset
+ graph</a>, or simply a <dfn>graph</dfn>, is a set of RDF triples.</p>
+<p>A <dfn>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>
+ A <dfn>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 with no blank
+<p>A <dfn>ground</dfn> RDF graph is one with no blank
nodes.</p>
-<p>A <dfn id="dfn-name-1">name</dfn> is an IRI or a literal.
+<p>A <dfn>name</dfn> is an IRI or a literal.
Note that a typed literal comprises
- two <a href="#dfn-name-1" class="internalDFN">name</a>s: itself and its internal type
+ two <a>name</a>s: itself and its internal type
IRI. </p>
-<p>A <dfn id="dfn-vocabulary-1">vocabulary</dfn> is a set of <a href="#dfn-name-1" class="internalDFN">name</a>s. The vocabulary of a graph is
+<p>A <dfn>vocabulary</dfn> is a set of <a>name</a>s. The vocabulary of a graph is
the set of names which occur as the subject, predicate or object of any triple
in the graph. IRIs which occur only inside typed literals
are not required to be in the vocabulary of the graph.</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,
+ an <dfn id="definst">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
in G.</p>
-<p>An <dfn id="dfn-instance-with-respect-to">instance with respect to</dfn> a vocabulary
- V is an <a href="#dfn-instance" class="internalDFN">instance</a> in which all the
- <a href="#dfn-name-1" class="internalDFN">name</a>s in the instance that were substituted
- for blank nodes in the original are <a href="#dfn-name-1" class="internalDFN">name</a>s
+<p>An <dfn>instance with respect to</dfn> a vocabulary
+ V is an <a>instance</a> in which all the
+ <a>name</a>s in the instance that were substituted
+ for blank nodes in the original are <a>name</a>s
from V.</p>
-<p>A <dfn id="dfn-proper-instance">proper instance</dfn> of a graph
- is an <a href="#dfn-instance" class="internalDFN">instance</a> in which a blank node has been replaced by a name, or two blank
+<p>A <dfn>proper instance</dfn> of a graph
+ is an <a>instance</a> in which a blank node has been replaced by a name, or two blank
nodes in the graph have been mapped into the same node in the instance. </p>
-<p>Any <a href="#dfn-instance" class="internalDFN">instance</a> of a graph in which a blank node is mapped to a new blank node
+<p >Any <a>instance</a> of a graph in which a blank node is mapped to a new blank node
not in the original graph is an instance of the original and also has it as
an instance, and this process can be iterated so that any 1:1 mapping between
blank nodes defines an instance of a graph which has the original graph as an
instance. Two such graphs, each an instance of the other but neither a proper
instance, which differ only in the identity of their blank nodes, are considered
- to be <dfn id="dfn-equivalent">equivalent</dfn>. Equivalent graphs are mutual instances with an invertible instance
+ to be <dfn>equivalent</dfn>. Equivalent 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 such equivalent graphs as identical.</p>
<p>Any set of graphs can be treated as a single graph simply by taking the union of the sets of triples. If two or more of the graphs share a blank node it will retain its identity when the union graph is formed. Graphs can share blank nodes only if they are derived from graphs described by documents or surface structures which share a single scope for blank node identifiers.</p>
<p class="issue">The Concepts document does not yet define blank node identifier scopes.</p>
-<p>We will refer to this process of forming the union of graphs as <dfn id="dfn-merging">merging</dfn>, and to the union graph as the <dfn id="dfn-merge">merge</dfn> of the original graphs. A merge may be represented by a new document or datastructure, or may be treated as a conceptual entity when processing RDF.</p>
+<p>We will refer to this process of forming the union of graphs as <dfn>merging</dfn>, and to the union graph as the <dfn>merge</dfn> of the original graphs. A merge may be represented by a new document or datastructure, or may be treated as a conceptual entity when processing RDF.</p>
<ul><li><p class="changenote"> The 2004 RDF 1.0 specification defined a process of 'standardizing apart' blank nodes to distinguish graph unions from graph merges. Standardizing apart blank node identifiers may still be needed at a concrete syntax level, but is no longer part of the underlying conceptual model of RDF. The earlier terminology is retained to avoid confusion, but now 'merging' simply means 'taking the union' at the graph syntax level. </p>
</li></ul>
-<p>An RDF graph is <dfn id="dfn-lean">lean</dfn> if it has no instance which is
+<p >An RDF graph is <dfn>lean</dfn> if it has no instance which is
a proper subgraph of the graph. 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 />
+<p ><code><ex:a> <ex:p> _:x .<br/>
_:y <ex:p> _:x .</code></p>
-<p>is not lean, but</p>
-<p><code><ex:a> <ex:p> _:x .<br />
+<p >is not lean, but</p>
+<p ><code><ex:a> <ex:p> _:x .<br/>
_:x <ex:p> _:x .</code></p>
-<p>is lean. </p>
+<p >is lean. </p>
- </div>
+ </section>
- <div id="simple-interpretations" class="section">
- <h2><span class="secno">4 </span> Simple Interpretations</h2>
+ <section>
+ <h2 id="simple"> Simple Interpretations</h2>
-<p>A <dfn id="dfn-simple-interpretation">simple interpretation</dfn> I is a structure consisting of:</p>
+<p>A <dfn>simple interpretation</dfn> I is a structure consisting of:</p>
<div class="tabletitle">Definition of a simple interpretation.</div>
<table border="1">
- <tbody><tr>
+ <tr>
<td class="semantictable"><p>1. A non-empty set IR of resources, called the domain or universe
of I.</p>
- <p>2. <span>A set IP, called the set of properties of I.</span></p>
+ <p>2. <span >A set IP, called the set of properties of I.</span></p>
<p>3. A mapping IEXT from IP into the powerset of IR x IR i.e. the
set of sets of pairs < x, y > with x and y in IR .</p>
<p>4. A mapping IS from IRIs into (IR union IP)</p>
<p>5. A partial mapping IL from literals into IR </p>
</td>
</tr>
- </tbody></table>
+ </table>
-<ul><li><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 <code>rdf:langString</code> for language-tagged strings. The full semantics for typed literals is given in the next section. </p>
+<ul><li><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 <code>rdf:langString</code> for language-tagged strings. The full semantics for typed literals is given in the next section. </p>
</li><li><p class="technote"> Interpretations are required to interpret all names, and are therefore infinite. This simplifies the exposition. However, RDF can be interpreted using finite structures, supporting decidable algorithms. Details are given in Appendix ///. </p>
</li></ul>
<p>IEXT(x), called
- the <dfn id="dfn-extension">extension</dfn> of x, is a
+ the <dfn>extension</dfn> of x, is a
set of pairs which identify the arguments for which the property is true,
that is, a binary relational extension.
</p>
@@ -694,7 +298,7 @@
<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>
- <h3 id="blank-nodes">Blank Nodes</h3>
+ <h3 id="blank_nodes">Blank Nodes</h3>
<p>Blank nodes are treated as simply indicating the existence of a thing, without using an IRI to identify any particular thing. They play a similar role to existentially quantified variables in a conventional logical notation. This is not the same as assuming that the blank node indicates an 'unknown' IRI.
@@ -702,7 +306,7 @@
<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 names, and A on blank nodes on the set: [I+A](x)=I(x) when x is a name 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. </p>
- <div class="tabletitle">Semantic condition for blank nodes.</div>
+ <div class="tabletitle">Semantic condition for blank nodes.</div>
<table border="1">
<tbody>
@@ -717,44 +321,52 @@
<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. Blank nodes themselves differ from other nodes in not being assigned a denotation by an interpretation, reflecting the intuition that they have no 'global' meaning outside the scope in which they occur.</p>
-<h3 id="intuitive-summary">Intuitive summary</h3>
+<h3 id="intuitions">Intuitive summary</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 scope as referring to things,</p><p>3. the IRIs in property position identify 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 identified by P. </p>
-<p>All semantic extensions of any vocabulary or higher-level notation encoded in RDF <em class="rfc2119" title="must">must</em> conform to these minimal truth conditions. Other semantic extensions may extend and add to these, but they <em class="rfc2119" title="must not">must not</em> over-ride or negate them. </p>
+<p>All semantic extensions of any vocabulary or higher-level notation encoded in RDF MUST conform to these minimal truth conditions. Other semantic extensions may extend and add to these, but they MUST NOT over-ride or negate them. </p>
- </div>
+ </section>
-<div id="simple-entailment" class="section"><h2><span class="secno">5 </span>Simple Entailment</h2>
+<section id="simpleentailment"><h2>Simple Entailment</h2>
<p class="issue">Should the 'explanatory' material in here be moved to the tutorial appendix? </p>
-<p>Following standard terminology, we say that I <dfn id="dfn-satisfies">satisfies</dfn> E when I(E)=true, and a set
- S of RDF graphs <dfn id="dfn-simply-entails">simply entails</dfn> a graph E when every interpretation
+<p>Following standard terminology, we say that I <dfn>satisfies</dfn> E when I(E)=true, and a set
+ S of RDF graphs <dfn>simply entails</dfn> a graph E when every interpretation
which satisfies every member of S also satisfies E. This means that it is always correct to infer E from S, even when one does not know what the names in the vocabulary actually mean. 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><a id="defvalid">Any process which constructs a graph E from
- some other graph(s) S is said to be (simply) <dfn id="dfn-valid">valid</dfn> if S
- simply entails E in every case, otherwise <dfn id="dfn-invalid.">invalid.</dfn></a></p>
+ some other graph(s) S is said to be (simply) <dfn>valid</dfn> if S
+ simply entails E in every case, otherwise <dfn>invalid.</dfn></a></p>
<p>The fact that an inference is valid should not be understood as meaning that the inference must be made, or that any process is obliged or required to make the inference; and 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 to be applied to RDF graphs. Entailment and validity are concerned solely with establishing the conditions on 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 and errors into otherwise correct 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>
-<p>Entailment refers only to the truth of RDF graphs, not to their suitability for any other purpose. It is possible for an RDF graph to be fitted for a given purpose and yet validly entail another graph which is not appropriate for the same purpose. An example is the RDF test cases manifest [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF-TESTCASES">RDF-TESTCASES</a></cite>] which is provided as an RDF document for user convenience. This document lists examples of correct entailments by describing their antecedents and conclusions. Considered as an RDF graph, the manifest validly entails a subgraph which omits the antecedents, and would therefore be incorrect if used as a test case manifest. This is not a violation of the RDF semantic rules, but it shows that the property of <em> "being a correct RDF test case manifest"</em> is not preserved under RDF entailment, and therefore cannot be described as an RDF semantic extension. Such entailment-risky uses of RDF should be restricted to cases, as here, where it is obvious to all parties what the intended special restrictions on entailment are, in contrast with the more normal case of using RDF for the open publication of data on the Web.</p>
+<p>Entailment refers only to the truth of RDF graphs, not to their suitability for any other purpose. It is possible for an RDF graph to be fitted for a given purpose and yet validly entail another graph which is not appropriate for the same purpose. An example is the RDF test cases manifest [[!RDF-TESTCASES]] which is provided as an RDF document for user convenience. This document lists examples of correct entailments by describing their antecedents and conclusions. Considered as an RDF graph, the manifest validly entails a subgraph which omits the antecedents, and would therefore be incorrect if used as a test case manifest. This is not a violation of the RDF semantic rules, but it shows that the property of <em> "being a correct RDF test case manifest"</em> is not preserved under RDF entailment, and therefore cannot be described as an RDF semantic extension. Such entailment-risky uses of RDF should be restricted to cases, as here, where it is obvious to all parties what the intended special restrictions on entailment are, in contrast with the more normal case of using RDF for the open publication of data on the Web.</p>
-<h3 id="some-basic-properties-of-simple-entailment.">Some basic properties of simple entailment. </h3>
+<h3 id="basic_properties">Some basic properties of simple entailment. </h3>
<p>The properties described here apply only to simple entailment, not to extended notions
of entailment introduced in later sections. Proofs
are given in <a>Appendix B</a>.</p>
-<p>Simple entailment can be recognized by relatively simple syntactic comparisons. The two basic forms of simply valid inference in RDF are, in logical terms, the inference from <code>(P and Q)</code> to <code>P</code>, and the inference from <code>foo(baz)</code> to <code>(exists (x) foo(x) ) </code>. The first corresponds to taking a subgraph of a graph, the second to replacing an IRI or literal with a blank node.</p>
+<p>Simple entailment can be recognized by relatively simple syntactic comparisons. The two basic forms of simply valid inference in RDF are, in logical terms, the inference from <code>(P and Q)</code> to <code>P</code>, and the inference from <code>foo(baz)</code> to <code>(exists (x) foo(x) ) </code>. The first corresponds to taking a subgraph of a graph, the second to replacing an IRI or literal with a blank node.</p>
<p><strong>Empty Graph Lemma.</strong> The empty set of triples is entailed by
- any graph, and does not entail any graph except itself. <a class="termref" href="#emptygraphlemmaprf">[Proof]</a></p>
+ any graph, and does not entail any graph except itself.
+<!-- <a href="#emptygraphlemmaprf" class="termref">[Proof]</a> -->
+</p>
<p><a id="subglem"><strong>Subgraph Lemma.</strong></a> A graph
- entails all its <a class="termref" href="#defsubg">subgraphs</a>. <a class="termref" href="#subglemprf">[Proof]</a></p>
+ entails all its subgraphs.
+<!-- <a href="#defsubg" class="termref"> subgraphs</a>. -->
+<!-- <a href="#subglemprf" class="termref">[Proof]</a> -->
+</p>
<p><a id="instlem"><strong>Instance Lemma.</strong></a> A graph
- is entailed by any of its <a class="termref" href="#definst">instances</a>.<a class="termref" href="#instlemprf"> [Proof]</a></p>
+ is entailed by any of its <a
+ href="#definst" class="termref">instances</a>.
+<!-- <a href="#instlemprf" class="termref"> [Proof]</a> -->
+</p>
<p>Obviously, the union of a set of graphs entails every member of the set, since they are all subgraphs of the union. However, if two or more graphs in the set share a blank node. then the set may fail to entail the union. For example, consider the graphs</p>
<p>
@@ -762,22 +374,28 @@
<p>and</p>
<p>
<code>:b :p _:x .</code></p>
-<p>Both graphs can be satisfied by an interpretation which does not satisfy their union, e.g. one with <br />IEXT(I(<code>:p</code>)) = {< I(<code>:a</code>),I(<code>:a</code>) >, < I(<code>:b</code>),I(<code>:b</code>) > }. This is because the mapping <code>_:x</code>/I(<code>:a</code>) works for the first graph, and the mapping <code>_:x</code>/I(<code>:b</code>) for the second graph, but there is no mapping which works for the combination. Neither graph is obliged to consider the full set of constraints on the blank node that are represented by their union. </p>
+<p>Both graphs can be satisfied by an interpretation which does not satisfy their union, e.g. one with <br/>IEXT(I(<code>:p</code>)) = {< I(<code>:a</code>),I(<code>:a</code>) >, < I(<code>:b</code>),I(<code>:b</code>) > }. This is because the mapping <code>_:x</code>/I(<code>:a</code>) works for the first graph, and the mapping <code>_:x</code>/I(<code>:b</code>) for the second graph, but there is no mapping which works for the combination. Neither graph is obliged to consider the full set of constraints on the blank node that are represented by their union. </p>
-<p>Say that a set S of graphs is <dfn id="dfn-segregated">segregated</dfn> when no two graphs in the set share a blank node.</p>
+<p>Say that a set S of graphs is <dfn>segregated</dfn> when no two graphs in the set share a blank node.</p>
<p><a id="mergelem"><strong>Merging lemma.</strong></a> The union
- of a segregated set S of RDF graphs is entailed by S, and entails every member of S. <a class="termref" href="#mergelemprf">[Proof]</a></p>
+ of a segregated set S of RDF graphs is entailed by S, and entails every member of S.
+<!-- <a href="#mergelemprf" class="termref">[Proof]</a> -->
+</p>
- <p>This means that a segregated set of graphs can be treated as <a class="termref" href="#glossEquivalent">equivalent</a> to its
- merge, a single graph, as far as the <a class="termref" href="#glossModeltheory">model theory</a> is
+ <p>This means that a segregated set of graphs can be treated as <a
+ href="#glossEquivalent" class="termref">equivalent</a> to its
+ merge, a single graph, as far as the <a
+ href="#glossModeltheory" class="termref">model theory</a> is
concerned. In general, we will not usually bother to distinguish between a set of graphs and the single graph formed by taking their union. </p>
<p>The main result for simple entailment is:</p>
<p><a id="interplemma"><strong>Interpolation Lemma.</strong>
- S entails a graph E if and only if a subgraph of S is an instance of E. </a><a class="termref" href="#interplemmaprf">[Proof]</a></p>
+ S entails a graph E if and only if a subgraph of S is an instance of E. </a>
+<!-- <a href="#interplemmaprf" class="termref">[Proof]</a> -->
+</p>
<p>The interpolation lemma completely characterizes simple entailment in syntactic
terms. To tell whether a set of RDF graphs simply entails another, check that
there is some instance of the entailed graph which is a subset of the merge
@@ -785,101 +403,113 @@
<p>This is clearly decidable, but it is also theoretically very hard 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. (///Refer to Jeremy Carroll.///) </p>
<p><a id="Anonlem1"><strong>Anonymity lemma.</strong></a> Suppose
- E is a <a href="#dfn-lean" class="internalDFN">lean</a> graph and E' is a proper instance of E. Then E does
- not entail E'. <a class="termref" href="#Anonlem1prf">[Proof]</a></p>
+ E is a <a>lean</a> graph and E' is a proper instance of E. Then E does
+ not entail E'.
+<!--
+<a href="#Anonlem1prf" class="termref">[Proof]</a>
+-->
+</p>
<p><strong><a id="monotonicitylemma"></a>Monotonicity
- Lemma</strong>. Suppose S is a subgraph of S' and S entails E. Then S' entails
- E.<a class="termref" href="#monotonicitylemmaprf"> [Proof]</a></p>
+ Lemma</strong>. Suppose S is a subgraph of S' and S entails E. Then S' entails E.
+<!-- <a href="#monotonicitylemmaprf" class="termref"> [Proof]</a> -->
+</p>
<p><strong><a id="compactlemma"></a>Compactness Lemma</strong>.
- If S entails E and E is a finite graph, then some finite subset S' of S entails
- E. <a class="termref" href="#compactlemmaprf"> [Proof]</a></p>
-</div>
+ If S entails E and E is a finite graph, then some finite subset S' of S entails E.
+<!-- <a href="#compactlemmaprf" class="termref"> [Proof]</a> -->
+</p>
+</section>
-<div id="skolemization" class="section"><h2><span class="secno">6 </span>Skolemization</h2>
-<p>Skolemization 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 ///Concepts#/// for a fuller discussion. </p>
+<section><h2 id="skolemization">Skolemization</h2>
+<p>Skolemization 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 ///Concepts#/// for a fuller discussion. </p>
<p> Suppose G is a graph containing blank nodes and sk is a skolemization mapping on the blank nodes in G, so that sk(G) is a skolemization of G. Then the semantic relationship between them can be summarized as follows. </p>
-<p>1. sk(G) simply entails G (by the <a class="termref" href="#instlem">instance lemma</a>, since sk(G) is an instance of G)</p>
-<p>2. G does not entail sk(G). <a class="termref" href="#skolemizeNentaillemmaprf"> [Proof]</a></p>
-<p>3. For any graph H, if sk(G) entails H then there is a graph H' such that G entails H' and H=sk(H') . <a class="termref" href="#skolemizeMainlemmaprf"> [Proof]</a></p>
-<p>4. 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.<a class="termref" href="#skolemizlemmaprf"> [Proof]</a> </p>
+<p>1. sk(G) simply entails G (by the <a href="#instlem" class="termref">instance lemma</a>, since sk(G) is an instance of G)</p>
+<p>2. G does not entail sk(G).
+<!-- <a href="#skolemizeNentaillemmaprf" class="termref"> [Proof]</a> -->
+</p>
+<p>3. For any graph H, if sk(G) entails H then there is a graph H' such that G entails H' and H=sk(H') .
+<!-- <a href="#skolemizeMainlemmaprf" class="termref"> [Proof]</a> -->
+</p>
+<p>4. 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.
+<!-- <a href="#skolemizlemmaprf" class="termref"> [Proof]</a> -->
+</p>
-<p>The second property means that a graph is not equivalent to its skolemization, so we cannot simply identify them. Nevertheless, they are in a strong sense almost interchangeable, as the next two properties attest. 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 equivalent to its skolemization, so we cannot simply identify them. Nevertheless, they are in a strong sense almost interchangeable, as the next two properties attest. 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>Skolemization means that it is possible to use RDF without using blank nodes without losing any real expressivity. Opinions differ on the merits of this strategy.</p>
-<ul><li><p class="technote">The more general notion of skolemization involving Skolem functions is not used in RDF as there are no universal quantifiers.</p>
+<ul><li><p class=technote>The more general notion of skolemization involving Skolem functions is not used in RDF as there are no universal quantifiers.</p>
</li></ul>
-</div>
+</section>
-<div id="literals-and-datatypes" class="section"><h2><span class="secno">7 </span>Literals and datatypes</h2>
-<ul><li><p class="changenote"> In the 2004 RDF 1.0 specification, datatype D-entailment was defined as a semantic extension 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>
+<section><h2 id="datatypes">Literals and datatypes</h2>
+<ul><li><p class="changenote"> In the 2004 RDF 1.0 specification, datatype D-entailment was defined as a semantic extension 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>
</li></ul>
-<p>RDF literals and datatypes are fully described in [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF11-CONCEPTS">RDF11-CONCEPTS</a></cite>]. In summary: RDF literals are either language-tagged strings, or datatyped literals which
-combine a string and an IRI identifying 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, and the literal refers to the value obtained by applying this mapping to the character string. If the 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 href="#dfn-lexical-to-value-mapping" class="internalDFN">lexical-to-value mapping</a>. Every literal with that type either refers to a value in the value space, or fails to refer at all. An <dfn id="dfn-ill-typed">ill-typed</dfn> literal is one whose datatype IRI is recognized, but whose character string is not in the domain of the datatype lexical-to-value mapping. Datatypes are indicated by IRIs.
+<p>RDF literals and datatypes are fully described in [[!RDF11-CONCEPTS]]. In summary: RDF literals are either language-tagged strings, or datatyped literals which
+combine a string and an IRI identifying a datatype. A datatype is understood to define a partial mapping, called the <dfn>lexical-to-value mapping</dfn>, from character strings to values, and the literal refers to the value obtained by applying this mapping to the character string. If the mapping gives no value for the literal string, then the literal has no referent. The <dfn>value space</dfn> of a datatype is the range of the <a>lexical-to-value mapping</a>. Every literal with that type either refers to a value in the value space, or fails to refer at all. An <dfn>ill-typed</dfn> literal is one whose datatype IRI is recognized, but whose character string is not in the domain of the datatype lexical-to-value mapping. Datatypes are indicated by IRIs.
</p>
-<p> Interpretations will vary according to which IRIs they recognize as denoting datatypes. We describe this using a parameter D on interpretations. where D is a set of IRIs that constitute the recognized datatype IRIs. IRIs listed in <a href="http://www.w3.org/TR/2013/WD-rdf11-concepts-20130115/#xsd-datatypes">///Concepts Section 5///</a> <em class="rfc2119" title="must">must</em> be interpreted as described there, and the IRI <code>rdf:plainLiteral</code> <em class="rfc2119" title="must">must</em> be interpreted to refer to the datatype defined in <a href="www.w3.org/TR/rdf-plain-literal/">///PlainLiteral///</a>. When other datatypes are used, the mapping between a recognized IRI and the datatype it refers to <em class="rfc2119" title="must">must</em> be specified unambiguously, and be fixed during all RDF transformations or manipulations.</p>
+<p> Interpretations will vary according to which IRIs they recognize as denoting datatypes. We describe this using a parameter D on interpretations. where D is a set of IRIs that constitute the recognized datatype IRIs. IRIs listed in <a href="http://www.w3.org/TR/2013/WD-rdf11-concepts-20130115/#xsd-datatypes">///Concepts Section 5///</a> MUST be interpreted as described there, and the IRI <code>rdf:plainLiteral</code> MUST be interpreted to refer to the datatype defined in [[!RDF-PLAINLITERAL]]. When other datatypes are used, the mapping between a recognized IRI and the datatype it refers to MUST be specified unambiguously, and be fixed during all RDF transformations or manipulations.</p>
<p>Language-tagged strings 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. (If datatype L2V mappings were defined on pairs of lexical values rather than strings, then the L2V mapping for <code>rdf:langString</code> would be the identity function on pairs of the form < unicode string, language tag >. But as they are not, we simply list this as a special case.)</p>
<p class="issue">This will require alignment with Concepts. rdf:langString may have an L2V mapping which is ignored by the semantics. Concepts currently states that it is not a datatype even though the IRI is a datatype IRI. </p>
-<p>RDF literal syntax allows any IRI to be used in a typed literal, even when it does not identify a datatype. Literals with an "unknown" datatype IRI which is not in the set of recognized datatypes, are treated like IRI names and assumed to denote some thing in the universe IR. </p>
-
-</div>
+<p>RDF literal syntax allows any IRI to be used in a typed literal, even when it does not identify a datatype. Literals with an "unknown" datatype IRI which is not in the set of recognized datatypes, are treated like IRI names and assumed to denote some thing in the universe IR. </p>
-<div id="d-interpretations-and-datatype-entailment" class="section"><h2><span class="secno">8 </span>D-interpretations and datatype entailment</h2>
-<p>Let D be a set of IRIs identifying datatypes. A <dfn id="dfn-simple--d-interpretation">(simple) D-interpretation</dfn> is a simple interpretation which satisfies the following conditions:</p>
+</section>
-<div class="tabletitle">Semantic conditions for datatyped literals.</div>
+<section id="D_interpretations"><h2>D-interpretations and datatype entailment</h2>
+<p>Let D be a set of IRIs identifying datatypes. A <dfn>(simple) D-interpretation</dfn> is a simple interpretation which satisfies the following conditions:</p>
+
+<div class="tabletitle">Semantic conditions for datatyped literals.</div>
<table border="1" class="semantictable">
<tbody>
<tr><td>If <code>rdf:langString</code> is in D, then for every language-tagged string E with lexical form sss and language tag ttt, IL(E)= < sss, ttt > </td></tr>
-<tr><td>For every other IRI aaa in D, and every literal "sss"^^aaa, IL("sss"^^aaa) = L2V(I(aaa))(sss)</td></tr>
+<tr><td>For every other IRI aaa in D, and every literal "sss"^^aaa, IL("sss"^^aaa) = L2V(I(aaa))(sss)</td></tr>
</tbody></table>
-<p>If the literal is ill-typed then the L2V 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 ill-typed literal will be D-inconsistent, i.e. false in every D-interpretation. This applies only to datatype IRIs in D; literals with "unknown" datatypes are not ill-typed and do not produce a D-inconsistency. </p>
+<p>If the literal is ill-typed then the L2V 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 ill-typed literal will be D-inconsistent, i.e. false in every D-interpretation. This applies only to datatype IRIs in D; literals with "unknown" datatypes are not ill-typed and do not produce a D-inconsistency. </p>
<ul><li><p class="changenote"> In the 2004 RDF 1.0 specification, ill-typed literals were required to denote a value in IR, and D-inconsistency could only be recognized by using the RDFS semantics. </p>
<p></p>
</li></ul>
-<h3 id="datatype-entailment">Datatype entailment</h3>
+<h3 id="D-entailment">Datatype entailment</h3>
-<p>A graph is (simply) <dfn id="dfn-d-satisfiable">D-satisfiable</dfn> when it has the value true in some D-interpretation, and a set S of graphs (simply) <dfn id="dfn-d-entails">D-entails</dfn> a graph G when every D-interpretation which makes S true also D-satisfies G.</p>
+<p>A graph is (simply) <dfn>D-satisfiable</dfn> when it has the value true in some D-interpretation, and a set S of graphs (simply) <dfn>D-entails</dfn> a graph G when every D-interpretation which makes S true also D-satisfies G.</p>
-<p> Unlike the case with simple interpretations, it is possible for a graph to have no satisfying D-interpretations, i.e. to be <dfn id="dfn-d-unsatisfiable">D-unsatisfiable</dfn>. A D-unsatisfiable graph D-entails any graph. </p>
+<p> Unlike the case with simple interpretations, it is possible for a graph to have no satisfying D-interpretations, i.e. to be <dfn>D-unsatisfiable</dfn>. A D-unsatisfiable graph D-entails any graph. </p>
-<p>In all of this language, 'D' is being used as a parameter to represent some set of datatype IRIs, and different D sets will yield different notions of satisfiability and entailment. The more datatypes are recognized, the stronger is the entailment, so that if D ⊂ E and S E-entails G then S must D-entail G. Simple entailment is { }-entailment, i.e. D-entailment when D is the empty set. If S D-entails G then S simply entails G, but not the reverse. </p>
+<p>In all of this language, 'D' is being used as a parameter to represent some set of datatype IRIs, and different D sets will yield different notions of satisfiability and entailment. The more datatypes are recognized, the stronger is the entailment, so that if D ⊂ E and S E-entails G then S must D-entail G. Simple entailment is { }-entailment, i.e. D-entailment when D is the empty set. If S D-entails G then S simply entails G, but not the reverse. </p>
<p>Several of the basic properties of simple entailment are also true for D-entailment, but the <a>interpolation lemma</a> is not true for <a>D-entailment</a>, since D-entailments
can hold because of particular properties of the lexical-to-value mappings of the recognized datatypes. For example, if D contains <code>xsd:integer</code> then </p>
-<p><code>aaa ppp "00025"^^xsd:integer .</code></p>
+<p><code>aaa ppp "00025"^^xsd:integer .</code></p>
<p>D-entails</p>
-<p><code>aaa ppp "25"^^xsd:integer .</code>
+<p><code>aaa ppp "25"^^xsd:integer .</code>
</p>
<p>
-</p><p>Ill-typed literals are the only form of simple D-contradiction, but datatypes can give rise to a variety of other contradictions when combined with the <a>RDFS vocabulary</a>, defined later.</p>
+<p>Ill-typed literals are the only form of simple D-contradiction, but datatypes can give rise to a variety of other contradictions when combined with the <a>RDFS vocabulary</a>, defined later.</p>
-</div>
-<div id="rdf-d-interpretations-and-rdf-entailment" class="section"><h2><span class="secno">9 </span>RDF-D Interpretations and RDF entailment</h2>
- <p>RDF-D interpretations impose extra semantic conditions on <code>xsd:string</code> and part of the infinite
+</section>
+<section><h2 id="rdf_d_interpretations">RDF-D Interpretations and RDF entailment</h2>
+ <p >RDF-D interpretations impose extra semantic conditions on <code>xsd:string</code> and part of the infinite
set of IRIs in the <code>rdf:</code> namespace.
-</p><p>An <dfn id="dfn-rdf-d-interpretation">rdf-D-interpretation</dfn> I is a D-interpretation where D includes <code>rdf:langString</code> and <code>xsd:string</code>, and which satisfies:</p>
+<p>An <dfn>rdf-D-interpretation</dfn> I is a D-interpretation 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">
+<table border="1">
<tbody>
<tr>
<td class="semantictable"><a id="rdfsemcond1"></a>x is
@@ -893,50 +523,50 @@
<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 />
- rdf:subject rdf:type rdf:Property .<br />
- rdf:predicate rdf:type rdf:Property .<br />
- rdf:object rdf:type rdf:Property .<br />
- rdf:first rdf:type rdf:Property .<br />
- rdf:rest rdf:type rdf:Property .<br />
- rdf:value rdf:type rdf:Property .<br />
- rdf:nil rdf:type rdf:List .<br />
- rdf:_1 rdf:type rdf:Property .<br />
- rdf:_2 rdf:type rdf:Property .<br />
- ... <br />
+ <table border="1">
+ <tr>
+ <td class="ruletable"><a id="RDF_axiomatic_triples"> </a><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/>
+ rdf:first rdf:type rdf:Property .<br/>
+ rdf:rest rdf:type rdf:Property .<br/>
+ rdf:value rdf:type rdf:Property .<br/>
+ rdf:nil rdf:type rdf:List .<br/>
+ rdf:_1 rdf:type rdf:Property .<br/>
+ rdf:_2 rdf:type rdf:Property .<br/>
+ ... <br/>
</code>
</td>
</tr>
- </tbody></table>
+ </table>
-<p>No other semantic constraints are imposed upon <a href="#dfn-rdf-d-interpretation" class="internalDFN">rdf-D-interpretation</a>s, so RDF imposes no particular normative meanings on the rest of the RDF vocabulary. Some consequences of this are discussed in <a>Appendix C</a></p>
+<p>No other semantic constraints are imposed upon <a>rdf-D-interpretation</a>s, so RDF imposes no particular normative meanings on the rest of the RDF vocabulary. Some consequences of this are discussed in <a>Appendix C</a></p>
-<p>An <em>rdf-interpretation</em>, or <em>RDF interpretation</em>, is an rdf-{<code>rdf:langString</code>, <code>xsd:string</code> }-interpretation, i.e. an rdf-D-Interpretation with a minimal set D. The datatypes <code>rdf:langString</code> and <code>xsd:string</code> <em class="rfc2119" title="must">must</em> be recognized by all RDF interpretations. </p><p>The RDF built-in datatypes <code>rdf:XMLLiteral</code> and <code>rdf:HTML</code> are defined in ///RDF Concepts///. RDF interpretations are not required to recognize these datatypes. </p>
+<p id="rdfinterpdef">An <em>rdf-interpretation</em>, or <em>RDF interpretation</em>, is an rdf-{<code>rdf:langString</code>, <code>xsd:string</code> }-interpretation, i.e. an rdf-D-Interpretation with a minimal set D. The datatypes <code>rdf:langString</code> and <code>xsd:string</code> MUST be recognized by all RDF interpretations. </p><p>The RDF built-in datatypes <code>rdf:XMLLiteral</code> and <code>rdf:HTML</code> are defined in [[!RDF11-CONCEPTS]]. RDF interpretations are not required to recognize these datatypes. </p>
-<h3 id="rdf-entailment"><a id="rdf_entail"></a>RDF entailment</h3>
+<h3><a id="rdf_entail"></a>RDF entailment</h3>
<p>S <i>rdf-D-entails</i> E when every rdf-D-interpretation which satisfies every
member of S also satisfies E. </p>
-<p>The lemmas in <a href="#entail"> Section 2</a> do not all apply to rdf-D-entailment:
- for example, all the rdf axioms are true in every <a class="termref" href="#rdfinterpdef">rdf-interpretation</a>, so are rdf-D-entailed by the empty graph,
- contradicting the <a class="termref" href="#interplemma">interpolation lemma</a> for rdf-D-entailment. Section //// gives rules that can be used to detect RDF entailment between RDF graphs. </p>
+<p>The lemmas for <a href="#simpleentailment">simple entailment</a> do not all apply to rdf-D-entailment:
+ for example, all the rdf axioms are true in every <a href="#rdfinterpdef" class="termref">rdf-interpretation</a>, so are rdf-D-entailed by the empty graph,
+ contradicting the <a href="#interplemma" class="termref">interpolation lemma</a> for rdf-D-entailment. Section //// gives rules that can be used to detect RDF entailment between RDF graphs. </p>
<p> The last semantic condition in the above table gives entailments of this form for recognized datatypes: </p>
-<p><code>aaa ppp "123"^^xsd:integer .</code></p>
+<p><code>aaa ppp "123"^^xsd:integer .</code></p>
<p>rdf-{<code>xsd:integer</code>}-entails</p>
-<code>aaa ppp _:x . <br /> _:x rdf:type xsd:integer .</code>
+<code>aaa ppp _:x . <br/> _:x rdf:type xsd:integer .</code>
-</div>
-<div id="rdfs-interpretations-and-rdfs-entailment" class="section"><h2><span class="secno">10 </span>RDFS Interpretations and RDFS entailment</h2>
-<p>RDF Schema [<cite><a href="#ref-rdf-vocabulary">RDF-VOCABULARY</a></cite>]
+</section>
+<section><h2 id="rdfs_interpretaitons">RDFS Interpretations and RDFS entailment</h2>
+<p>RDF Schema [[RDF-SCHEMA]]
extends RDF to a larger <a id="defRDFSV"></a>vocabulary
with more complex semantic constraints:</p>
@@ -963,10 +593,11 @@
and <code>rdfs:subPropertyOf</code>. Other than this, the formal semantics does
not constrain their meanings.)</p>
<p>Although not strictly necessary, it is convenient to state the RDFS semantics
- in terms of a new semantic construct, a <a class="termref" href="#glossClass"><em>class</em></a>, i.e. a resource which represents
+ in terms of a new semantic construct, a <a
+ href="#glossClass" class="termref"><em>class</em></a>, i.e. a resource which represents
a set of things in the universe which all have that class as the value of their
<code>rdf:type</code> property. Classes are defined to be things of type <code>rdfs:Class</code>,
- and <span>the set of all classes in an interpretation will be called IC</span>.
+ and <span >the set of all classes in an interpretation will be called IC</span>.
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.
@@ -974,13 +605,13 @@
</p>
-<p><a id="rdfsinterpdef"></a> An <i>rdfs-D-interpretation</i> is an <a class="termref" href="#rdfinterpdef">rdf-D-interpretation</a> I
+<p><a id="rdfsinterpdef"></a> An <i>rdfs-D-interpretation</i> is an <a href="#rdfinterpdef" class="termref">rdf-D-interpretation</a> I
which satisfies the semantic conditions in the following table, and satisfies all the triples in the subsequent table of <em>RDFS axiomatic triples</em>. As before, an <em>rdfs-interpretation</em>, or <em>RDFS interpretation</em>, is an rdfs-D-interpretation with D= {<code>xsd:string</code>, <code>rdf:langString</code> }.</p>
<p class="issue">This table has redundancies. I am inclined to leave them alone, as it takes quite a lot of thought to figure out some of the consequences when we only give non-redundant conditions. </p>
<div class="tabletitle">RDFS semantic conditions.</div>
- <table border="1">
- <tbody><tr>
+ <table border="1">
+ <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>
<p>IC is defined to be ICEXT(I(<code>rdfs:Class</code>))</p>
@@ -1033,17 +664,17 @@
<tr>
<td class="semantictable"><p><a id="rdfssemcond9"></a>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>
+ 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/>
+ </td>
</tr>
<tr>
<td class="semantictable"><p><a id="rdfssemcond10"></a>If
- x is in ICEXT(I(<code>rdfs:Datatype</code>)) then <span>< x,
+ 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>
+ </table>
<p></p>
@@ -1052,114 +683,114 @@
<p><a id="RDFS_axiomatic_triples"> </a>
</p>
<div class="tabletitle">RDFS axiomatic triples.</div>
- <table border="1">
+ <table border="1">
- <tbody><tr>
+ <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 />
- rdfs:subPropertyOf rdfs:domain rdf:Property .<br />
+ <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/>
+ rdfs:subPropertyOf rdfs:domain rdf:Property .<br/>
<a id="axtripleforproof1"></a>rdfs:subClassOf rdfs:domain
- rdfs:Class .<br />
- rdf:subject rdfs:domain rdf:Statement .<br />
- rdf:predicate rdfs:domain rdf:Statement .<br />
- rdf:object rdfs:domain rdf:Statement .<br />
- rdfs:member rdfs:domain rdfs:Resource . <br />
- rdf:first rdfs:domain rdf:List .<br />
- rdf:rest rdfs:domain rdf:List .<br />
- rdfs:seeAlso rdfs:domain rdfs:Resource .<br />
- rdfs:isDefinedBy rdfs:domain rdfs:Resource .<br />
- rdfs:comment rdfs:domain rdfs:Resource .<br />
- rdfs:label rdfs:domain rdfs:Resource .<br />
- rdf:value rdfs:domain rdfs:Resource .<br />
- <br />
- rdf:type rdfs:range rdfs:Class .<br />
- rdfs:domain rdfs:range rdfs:Class .<br />
- rdfs:range rdfs:range rdfs:Class .<br />
- rdfs:subPropertyOf rdfs:range rdf:Property .<br />
+ rdfs:Class .<br/>
+ rdf:subject rdfs:domain rdf:Statement .<br/>
+ rdf:predicate rdfs:domain rdf:Statement .<br/>
+ rdf:object rdfs:domain rdf:Statement .<br/>
+ rdfs:member rdfs:domain rdfs:Resource . <br/>
+ rdf:first rdfs:domain rdf:List .<br/>
+ rdf:rest rdfs:domain rdf:List .<br/>
+ rdfs:seeAlso rdfs:domain rdfs:Resource .<br/>
+ rdfs:isDefinedBy rdfs:domain rdfs:Resource .<br/>
+ rdfs:comment rdfs:domain rdfs:Resource .<br/>
+ rdfs:label rdfs:domain rdfs:Resource .<br/>
+ rdf:value rdfs:domain rdfs:Resource .<br/>
+ <br/>
+ rdf:type rdfs:range rdfs:Class .<br/>
+ rdfs:domain rdfs:range rdfs:Class .<br/>
+ rdfs:range rdfs:range rdfs:Class .<br/>
+ rdfs:subPropertyOf rdfs:range rdf:Property .<br/>
<a id="axtripleforproof2"></a>rdfs:subClassOf rdfs:range
- rdfs:Class .<br />
- rdf:subject rdfs:range rdfs:Resource .<br />
- rdf:predicate rdfs:range rdfs:Resource .<br />
- rdf:object rdfs:range rdfs:Resource .<br />
- rdfs:member rdfs:range rdfs:Resource .<br />
- rdf:first rdfs:range rdfs:Resource .<br />
- rdf:rest rdfs:range rdf:List .<br />
- rdfs:seeAlso rdfs:range rdfs:Resource .<br />
- rdfs:isDefinedBy rdfs:range rdfs:Resource .<br />
- rdfs:comment rdfs:range rdfs:Literal .<br />
- rdfs:label rdfs:range rdfs:Literal .<br />
- rdf:value rdfs:range rdfs:Resource .<br />
- <br />
- rdf:Alt rdfs:subClassOf rdfs:Container .<br />
- rdf:Bag rdfs:subClassOf rdfs:Container .<br />
- rdf:Seq rdfs:subClassOf rdfs:Container .<br />
- rdfs:ContainerMembershipProperty rdfs:subClassOf rdf:Property .<br />
- <br />
- rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso .<br />
- <br />
+ rdfs:Class .<br/>
+ rdf:subject rdfs:range rdfs:Resource .<br/>
+ rdf:predicate rdfs:range rdfs:Resource .<br/>
+ rdf:object rdfs:range rdfs:Resource .<br/>
+ rdfs:member rdfs:range rdfs:Resource .<br/>
+ rdf:first rdfs:range rdfs:Resource .<br/>
+ rdf:rest rdfs:range rdf:List .<br/>
+ rdfs:seeAlso rdfs:range rdfs:Resource .<br/>
+ rdfs:isDefinedBy rdfs:range rdfs:Resource .<br/>
+ rdfs:comment rdfs:range rdfs:Literal .<br/>
+ rdfs:label rdfs:range rdfs:Literal .<br/>
+ rdf:value rdfs:range rdfs:Resource .<br/>
+ <br/>
+ rdf:Alt rdfs:subClassOf rdfs:Container .<br/>
+ rdf:Bag rdfs:subClassOf rdfs:Container .<br/>
+ rdf:Seq rdfs:subClassOf rdfs:Container .<br/>
+ rdfs:ContainerMembershipProperty rdfs:subClassOf rdf:Property .<br/>
+ <br/>
+ rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso .<br/>
+ <br/>
- rdfs:Datatype rdfs:subClassOf rdfs:Class .<br />
- <br />
- rdf:_1 rdf:type rdfs:ContainerMembershipProperty .<br />
- <span>rdf:_1 rdfs:domain rdfs:Resource .<br />
- rdf:_1 rdfs:range rdfs:Resource .</span> <br />
- rdf:_2 rdf:type rdfs:ContainerMembershipProperty .<br />
- rdf:_2 rdfs:domain rdfs:Resource .<br />
- rdf:_2 rdfs:range rdfs:Resource . <br />
- </code>... <br /> </td>
+ rdfs:Datatype rdfs:subClassOf rdfs:Class .<br/>
+ <br/>
+ rdf:_1 rdf:type rdfs:ContainerMembershipProperty .<br/>
+ <span >rdf:_1 rdfs:domain rdfs:Resource .<br/>
+ rdf:_1 rdfs:range rdfs:Resource .</span> <br/>
+ rdf:_2 rdf:type rdfs:ContainerMembershipProperty .<br/>
+ rdf:_2 rdfs:domain rdfs:Resource .<br/>
+ rdf:_2 rdfs:range rdfs:Resource . <br/>
+ </code>... <br/> </td>
</tr>
- </tbody></table>
+ </table>
<ul><li><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>
</li></ul>
-<p>Since I is an <a class="termref" href="#rdfinterpdef">rdf-interpretation</a>, the first condition implies that IP
+<p>Since I is an <a href="#rdfinterpdef" class="termref">rdf-interpretation</a>, the first condition implies that IP
= ICEXT(I(<code>rdf:Property</code>)).</p>
<p>The semantic conditions on rdf-D-interpretations, together with the RDFS conditions on ICEXT, mean that every recognized datatype can be treated as an RDFS class whose extension is the value space of the datatype, and every literal with that datatype either fails to refer (if the literal is ill-typed) or else refers to a value in that class.</p>
<p>These axioms and conditions 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>.
- Other triples which must be true in all <a class="termref" href="#rdfsinterpdef">rdfs-interpretation</a>s
+ Other triples which must be true in all <a href="#rdfsinterpdef" class="termref">rdfs-interpretation</a>s
include the following:</p>
<div class="tabletitle">Some rdfs-valid triples.</div>
-<table border="1">
- <tbody><tr>
- <td class="ruletable"><code>rdfs:Resource rdf:type rdfs:Class .<br />
- rdfs:Class rdf:type rdfs:Class .<br />
- rdfs:Literal rdf:type rdfs:Class .<br />
- rdf:XMLLiteral rdf:type rdfs:Class .<br />
-rdf:HTML rdf:type rdfs:Class .<br />
- rdfs:Datatype rdf:type rdfs:Class .<br />
- rdf:Seq rdf:type rdfs:Class .<br />
- rdf:Bag rdf:type rdfs:Class .<br />
- rdf:Alt rdf:type rdfs:Class .<br />
- rdfs:Container rdf:type rdfs:Class .<br />
- rdf:List rdf:type rdfs:Class .<br />
- rdfs:ContainerMembershipProperty rdf:type rdfs:Class .<br />
- rdf:Property rdf:type rdfs:Class .<br />
- rdf:Statement rdf:type rdfs:Class .<br />
- <br />
- rdfs:domain rdf:type rdf:Property .<br />
- rdfs:range rdf:type rdf:Property .<br />
- rdfs:subPropertyOf rdf:type rdf:Property .<br />
- rdfs:subClassOf rdf:type rdf:Property .<br />
- rdfs:member rdf:type rdf:Property .<br />
- rdfs:seeAlso rdf:type rdf:Property .<br />
- rdfs:isDefinedBy rdf:type rdf:Property .<br />
- rdfs:comment rdf:type rdf:Property .<br />
- rdfs:label rdf:type rdf:Property .<br />
+<table border="1">
+ <tr>
+ <td class="ruletable"><code>rdfs:Resource rdf:type rdfs:Class .<br/>
+ rdfs:Class rdf:type rdfs:Class .<br/>
+ rdfs:Literal rdf:type rdfs:Class .<br/>
+ rdf:XMLLiteral rdf:type rdfs:Class .<br/>
+rdf:HTML rdf:type rdfs:Class .<br/>
+ rdfs:Datatype rdf:type rdfs:Class .<br/>
+ rdf:Seq rdf:type rdfs:Class .<br/>
+ rdf:Bag rdf:type rdfs:Class .<br/>
+ rdf:Alt rdf:type rdfs:Class .<br/>
+ rdfs:Container rdf:type rdfs:Class .<br/>
+ rdf:List rdf:type rdfs:Class .<br/>
+ rdfs:ContainerMembershipProperty rdf:type rdfs:Class .<br/>
+ rdf:Property rdf:type rdfs:Class .<br/>
+ rdf:Statement rdf:type rdfs:Class .<br/>
+ <br/>
+ rdfs:domain rdf:type rdf:Property .<br/>
+ rdfs:range rdf:type rdf:Property .<br/>
+ rdfs:subPropertyOf rdf:type rdf:Property .<br/>
+ rdfs:subClassOf rdf:type rdf:Property .<br/>
+ rdfs:member rdf:type rdf:Property .<br/>
+ rdfs:seeAlso rdf:type rdf:Property .<br/>
+ rdfs:isDefinedBy rdf:type rdf:Property .<br/>
+ rdfs:comment rdf:type rdf:Property .<br/>
+ rdfs:label rdf:type rdf:Property .<br/>
</code><code></code></td>
</tr>
-</tbody></table>
+</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>
-<h3 id="a-note-on-rdfs-literal">A note on rdfs:Literal</h3>
-<p>The class <code>rdfs:Literal</code> is not the class of literals, but rather that of literal <em>values</em>. For example, LV does not contain the literal <code>"24"^^xsd:integer</code> (although it might contain the string '<code>"24"^^http://www.w3.org/2001/XMLSchema#integer</code>' ) but it does contain the number twenty-four.</p>
+<h3 id="rdfs_literal">A note on rdfs:Literal</h3>
+<p>The class <code>rdfs:Literal</code> is not the class of literals, but rather that of literal <em>values</em>. For example, LV does not contain the literal <code>"24"^^xsd:integer</code> (although it might contain the string '<code>"24"^^http://www.w3.org/2001/XMLSchema#integer</code>' ) but it does contain the number twenty-four.</p>
<p>A triple of the form</p>
@@ -1169,51 +800,54 @@
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. Similarly, blank nodes may range over literal values. </p>
-<h3 id="rdfs-entailment">RDFS Entailment</h3>
-<p>S <i>rdfs-D-entails</i> E when every <a class="termref" href="#rdfsinterpdef">rdfs-D-interpretation</a>
+<h3 id="rdfs_entailment">RDFS Entailment</h3>
+<p>S <i>rdfs-D-entails</i> E when every <a href="#rdfsinterpdef" class="termref">rdfs-D-interpretation</a>
which satisfies every member of S also satisfies E. RDFS entailment is rdfs-{<code>rdf:langString</code>, <code>xsd:string</code> }-entailment, i.e. rdfs-D-entailment with a minimal D. </p>
-<p> Since every <a class="termref" href="#rdfsinterpdef">rdfs-D-interpretation</a> is an <a class="termref" href="#rdfinterpdef">rdf-D-interpretation</a>, if S rdfs-D-entails
+<p> Since every <a href="#rdfsinterpdef" class="termref">rdfs-D-interpretation</a> is an <a href="#rdfinterpdef" class="termref">rdf-D-interpretation</a>, if S rdfs-D-entails
E then S also rdf-D-entails 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> <code>aaa rdf:type rdfs:Resource .</code></p>
-<p>where aaa is an IRI, are true in all <a class="termref" href="#rdfsinterpdef">rdfs-interpretation</a>s.</p>
+<p>where aaa is an IRI, are true in all <a href="#rdfsinterpdef" class="termref">rdfs-interpretation</a>s.</p>
-</div>
-<div id="monotonicity-of-semantic-extensions" class="section"><h2><span class="secno">11 </span>Monotonicity of semantic extensions </h2>
+</section>
+<section><h2 id="monotonicity">Monotonicity of semantic extensions </h2>
<p>Given a set of RDF graphs, there are various ways in which one can 'add' information
to it. Any of the graphs may have some triples added to it; the set of graphs
may be extended by extra graphs; or the vocabulary of the graph may be interpreted
- relative to a stronger notion of <a class="termref" href="#vocabulary_entail">vocabulary entailment</a>, i.e. with a larger set
+ relative to a stronger notion of
+entailment,
+<!-- <a href="#vocabulary_entail" class="termref">vocabulary entailment</a>, -->
+ i.e. with a larger set
of semantic conditions understood to be imposed on the interpretations. All
of these can be thought of as an addition of information, and may make more
- entailments hold than held before the change. All of these additions are <a class="termref" href="#glossMonotonic"><em>monotonic</em></a>,
+ entailments hold than held before the change. All of these additions are <a href="#glossMonotonic" class="termref"><em>monotonic</em></a>,
in the sense that entailments which hold before the addition of information,
also hold after it. We can sum up this in a single lemma:</p>
-<p><strong><a id="GeneralMonotonicityLemma"></a>General monotonicity lemma</strong>. Suppose
+<p ><strong><a id="GeneralMonotonicityLemma"></a>General monotonicity lemma</strong>. Suppose
that S, S' are sets of RDF graphs with every member of S a subset
of some member of S'. Suppose that Y indicates a semantic extension
- of X, S X-entails E, and S and
+ of X, S X-entails E, and S and
E satisfy any syntactic restrictions of Y. Then S' Y-entails E.</p>
-<p>In particular, if D' is a <a class="termref" href="#defDatatypeMap">datatype map</a>, D a subset of D' and if S <a class="termref" href="#D_entailment"> D-entail</a>s
+<p >In particular, if D' is a set of IRIs identifying datatypes, D a subset of D' and if S <a href="#D_entailment" class="termref"> D-entail</a>s
E then S also D'-entails E. </p>
-</div>
+</section>
-<div class="informative section" id="extensional-rdfs-semantic-conditions--informative"><h2><span class="secno">12 </span>Extensional RDFS Semantic Conditions (Informative)</h2><p><em>This section is non-normative.</em></p>
+<section class="informative"><h2 id="extensional_rdfs">Extensional RDFS Semantic Conditions (Informative)</h2>
<p class="issue">Is this section useful, or is it more likely to be confusing? Editor is inclined to delete it. </p>
<p>The semantics given above is deliberately chosen to be the weakest 'reasonable'
- interpretation of the RDFS vocabulary. Semantic extensions <em class="rfc2119" title="may">may</em>
+ interpretation of the RDFS vocabulary. Semantic extensions MAY
strengthen the range, domain, subclass and subproperty semantic conditions to
- the following '<a href="#glossExtensional" class="termref">extensional</a>'
+ the following '<a class="termref" href="#glossExtensional">extensional</a>'
versions:</p>
<div class="tabletitle">Extensional alternatives for some RDFS semantic conditions.</div>
<table border="1">
- <tbody><tr>
+ <tr>
<td class="semantictable"> <p>< x,y > is in IEXT(I(<code>rdfs:subClassOf</code>))
if and only if x and y are in IC and ICEXT(x) is a subset of ICEXT(y)</p></td>
</tr>
@@ -1229,37 +863,39 @@
<td class="semantictable"> <p>< x,y > is in IEXT(I(<code>rdfs:domain</code>))
if and only if (if <u,v> is in IEXT(x) then u is in ICEXT(y))</p></td>
</tr>
-</tbody></table>
+</table>
<p>which would guarantee that the subproperty and subclass properties were transitive
and reflexive, and would also have further consequences. </p>
<ul><li><p class="technote">These stronger conditions would be trivially satisfied when properties are
identified with property extensions, classes with class extensions, and <code>rdfs:SubClassOf</code>
- understood to mean subset, and hence would be satisfied by an <a class="termref" href="#glossExtensional">extensional</a> semantics
+ understood to mean subset, and hence would be satisfied by an <a href="#glossExtensional" class="termref">extensional</a> semantics
for RDFS. In some ways the extensional versions provide a simpler semantics,
- but they require more complex inference rules. The <a class="termref" href="#glossIntensional">intensional</a> semantics described
+ but they require more complex inference rules. The <a href="#glossIntensional" class="termref">intensional</a> semantics described
in the main text provides for most common uses of subclass and subproperty assertions,
- and allows for simpler implementations of a <a class="termref" href="#glossComplete">
- complete</a> set of RDFS entailment rules, described in <a class="termref" href="#RDFSRules"> ////</a>.</p>
+ and allows for simpler implementations of a <a href="#glossComplete" class="termref">
+ complete</a> set of RDFS entailment rules.
+<!-- , described in <a href="#RDFSRules" class="termref"> ////</a>. -->
+</p>
</li></ul>
-</div>
+</section>
-<div class="informative section" id="entailment-rules--informative"><h2><span class="secno">13 </span>Entailment Rules (Informative)</h2><p><em>This section is non-normative.</em></p>
-<p class="issue"> The inference rules need to be rewritten using the convention that they apply to a syntactic generalization of RDF that allows literals in subject position. This will take some editorial work to complete but should be easier to understand once it is done. The hard work has already been done by terHorst. <br /> <br /> I do not plan to reproduce the completeness proofs which were in the RDF 2004 document. They were unreadable, intimidating, buggy and unnecessary. </p>
+<section class="informative"><h2 id="entailment_rules">Entailment Rules (Informative)</h2>
+<p class="issue"> The inference rules need to be rewritten using the convention that they apply to a syntactic generalization of RDF that allows literals in subject position. This will take some editorial work to complete but should be easier to understand once it is done. The hard work has already been done by terHorst. <br/> <br/> I do not plan to reproduce the completeness proofs which were in the RDF 2004 document. They were unreadable, intimidating, buggy and unnecessary. </p>
-</div>
+</section>
-<div id="MTintro" class="appendix section"><h2><span class="secno">A </span>Introduction to model theory (Informative)</h2>
+<section class="appendix" id="MTintro"><h2 id="model_theory">Introduction to model theory (Informative)</h2>
///
-</div>
-<div id="proofs" class="appendix section"><h2><span class="secno">B </span>Proofs of Lemmas (Informative)</h2>
+</section>
+<section class="appendix" id="proofs"><h2 id="proofs">Proofs of Lemmas (Informative)</h2>
///interpolation lemma is now slightly less trivial to prove. Check for possible consequences of this.///
-</div>
-<div id="whatnot" class="appendix section"><h2><span class="secno">C </span>What the semantics does not do (Informative)</h2>
+</section>
+<section class="appendix" id="whatnot"><h2 id="non_semantics">What the semantics does not do (Informative)</h2>
<p class="issue">Something in here about datasets having no specified semantics, and why. Why using a graph name need not refer to the graph.</p>
-<h3 id="the-rdf-vocabulary">The RDF vocabulary</h3>
+<h3 id="rdf_vocabulary">The RDF vocabulary</h3>
<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. In this appendix we briefly review the intended meanings of this vocabulary. </p>
@@ -1270,10 +906,10 @@
processes to check formal RDF entailment. For example, implementations may decide
to use special procedural techniques to implement the RDF collection vocabulary.</p>
-<h3 id="reification"><a id="Reif">Reification</a></h3>
+<h3><a id="Reif">Reification</a></h3>
<div class="c1">
- <table border="1">
+ <table border="1">
<tbody>
<tr>
<td class="othertable"><strong>RDF reification vocabulary</strong></td>
@@ -1295,12 +931,13 @@
<p>and suppose that this graph is identified by the IRI <code>ex:graph1</code>. Exactly how this identification is achieved is external to the RDF model, but it might be by the IRI resolving to a concrete syntax document describing the graph, or by the IRI being the associated name of a named graph in a dataset. Assuming that the IRI can be used to refer to the triple, then the reification vocabulary allows us to describe the first graph in another graph:</p>
- <p><code><ex:graph1> rdf:type rdf:Statement .<br />
- <ex:graph1> rdf:subject <ex:a> .<br />
- <ex:graph1> rdf:predicate <ex:b> .<br />
+ <p><code><ex:graph1> rdf:type rdf:Statement .<br/>
+ <ex:graph1> rdf:subject <ex:a> .<br/>
+ <ex:graph1> rdf:predicate <ex:b> .<br/>
<ex:graph1> rdf:object <ex:c> .</code></p>
- <p>The second graph is called a <i><a class="termref" href="#glossReify"><em>reification</em></a></i> of the triple in the first
+ <p>The second graph is called a <i><a href="#glossReify"
+ class="termref"><em>reification</em></a></i> of the triple in the first
graph.</p>
<p> Reification is not a form of quotation. Rather, the reification describes the
relationship between a token of a triple and the resources that the triple refers
@@ -1332,14 +969,14 @@
entail that the same property holds of another such entity, even if
it has the same components. For example,</p>
- <p><code>_:xxx rdf:type rdf:Statement .<br />
- _:xxx rdf:subject <ex:subject> .<br />
- _:xxx rdf:predicate <ex:predicate> .<br />
- _:xxx rdf:object <ex:object> .<br />
- _:yyy rdf:type rdf:Statement .<br />
- _:yyy rdf:subject <ex:subject> .<br />
- _:yyy rdf:predicate <ex:predicate> .<br />
- _:yyy rdf:object <ex:object> .<br />
+ <p><code>_:xxx rdf:type rdf:Statement .<br/>
+ _:xxx rdf:subject <ex:subject> .<br/>
+ _:xxx rdf:predicate <ex:predicate> .<br/>
+ _:xxx rdf:object <ex:object> .<br/>
+ _:yyy rdf:type rdf:Statement .<br/>
+ _:yyy rdf:subject <ex:subject> .<br/>
+ _:yyy rdf:predicate <ex:predicate> .<br/>
+ _:yyy rdf:object <ex:object> .<br/>
_:xxx <ex:property> <ex:foo> .</code></p>
<p>does not entail</p>
@@ -1347,7 +984,7 @@
<p><code>_:yyy <ex:property> <ex:foo> .</code></p>
-<h4 id="rdf-containers"><a id="Containers">RDF containers</a></h4>
+<h4 a="containers"><a id="Containers">RDF containers</a></h4>
<table border="1">
<tbody>
@@ -1381,7 +1018,8 @@
characterize the container type and give partial information about
the members of a container. Since the RDF container vocabulary is
so limited, many 'natural' assumptions concerning RDF containers
- are not formally sanctioned by the RDF <a class="termref" href="#glossModeltheory">model theory</a>. This should not be taken as
+ are not formally sanctioned by the RDF <a href="#glossModeltheory"
+ class="termref">model theory</a>. This should not be taken as
meaning that these assumptions are false, but only that RDF does
not formally entail that they must be true.</p>
@@ -1406,16 +1044,16 @@
<p>RDF does not support any entailments which could arise from enumerating
the elements of an <code>rdf:Bag</code> in a different order. For example,</p>
- <p><code>_:xxx rdf:type rdf:Bag .<br />
- _:xxx rdf:_1 <ex:a> .<br />
+ <p><code>_:xxx rdf:type rdf:Bag .<br/>
+ _:xxx rdf:_1 <ex:a> .<br/>
_:xxx rdf:_2 <ex:b> .</code></p>
<p>does not entail</p>
- <p><code>_:xxx rdf:_1 <ex:b> .<br />
+ <p><code>_:xxx rdf:_1 <ex:b> .<br/>
_:xxx rdf:_2 <ex:a> .</code></p>
- <p>Notice that if this conclusion were <a href="#dfn-valid" class="internalDFN">valid</a>, then the result of
+ <p>Notice that if this conclusion were <a>valid</a>, then the result of
conjoining it to the original graph would be <a>entailed</a> 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>
@@ -1426,8 +1064,8 @@
the three container classes are disjoint, so that for example
it is not a <a>contradiction</a> 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 />
+ <p><code>_:xxx rdf:type rdf:Seq.<br/>
+ _:xxx rdf:_1 <ex:a> .<br/>
_:xxx rdf:_3 <ex:c> .</code></p>
<p>does not entail</p>
@@ -1442,9 +1080,9 @@
only finitely many members.</p>
-<h4 id="rdf-collections"><a id="collections"></a>RDF collections</h4>
+<a id="collections"></a>RDF collections</h4>
- <table border="1">
+ <table border="1">
<tbody>
<tr>
<td class="othertable"><strong>RDF Collection Vocabulary</strong></td>
@@ -1466,9 +1104,9 @@
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 />
+<code><br/>
+ <br/>
+ _:c1 rdf:first aaa .<br/>
_:c1 rdf:rest _:c2</code></p>
@@ -1482,27 +1120,27 @@
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 />
- _:c1 rdf:first <ex:aaa> .<br />
- _:c1 rdf:rest _:c2 .<br />
- <span> _:c2 rdf:first</span> <ex:bbb> .<br />
+<br/><br/>
+ _:c1 rdf:first <ex:aaa> .<br/>
+ _:c1 rdf:rest _:c2 .<br/>
+ <span > _:c2 rdf:first</span> <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 />
+<p><code>_:c3 rdf:first <ex:bbb> .<br/>
+ _:c3 rdf:rest _:c4 .<br/>
+ <span >_:c4 rdf:first</span> <ex:aaa> .<br/>
_:c4 rdf:rest rdf:nil .
</code></p>
- <p>Also, RDF imposes no '<a class="termref" href="#glossWellformed">well-formedness</a>' conditions on the use of this
+ <p>Also, RDF imposes no 'well-formedness' conditions on the use of this
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 />
+<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>
@@ -1510,9 +1148,9 @@
by failing to specify its <code>rdf:rest</code> property value.</p>
-<p>Semantic extensions <em class="rfc2119" title="may">may</em>
+<p>Semantic extensions MAY
place extra syntactic well-formedness restrictions on the use of this vocabulary
- in order to rule out such graphs. They <em class="rfc2119" title="may">may</em>
+ 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
@@ -1525,10 +1163,10 @@
the <code>rdf:rest</code> property, be of <code>rdf:type rdf:List</code>. </p>
-<h3 id="rdf-value"><a id="rdfValue"></a>rdf:value</h3>
+<h3><a id="rdfValue"></a>rdf:value</h3>
<p>The intended use for <code>rdf:value</code> is <a href="http://www.w3.org/TR/rdf-primer/#rdfvalue">explained
intuitively</a> in the RDF Primer
- document [<cite><a class="bibref" rel="biblioentry" href="#bib-RDF-PRIMER">RDF-PRIMER</a></cite>]. It is typically
+ document [[RDF-PRIMER]]. It is typically
used to identify a 'primary' or 'main' value of a property which has several
values, or has as its value a complex entity with several facets or properties
of its own.</p>
@@ -1539,10 +1177,14 @@
Even when the intended meaning is clear from the context in the original graph document, it may be
lost when graphs are merged or when conclusions are inferred.</p>
-</div>
-<div id="glossary" class="appendix section"><h2><span class="secno">D </span>Glossary of Terms (Informative)</h2>
- <p><strong><a id="glossAntecedent"></a>Antecedent</strong> (n.) In an <a class="termref" href="#glossInference">inference</a>, the
- expression(s) from which the <a class="termref" href="#glossConsequent">conclusion</a> is derived. In an <a class="termref" href="#glossEntail">entailment</a> relation, the
+</section>
+<section class="appendix" id="glossary"><h2>Glossary of Terms (Informative)</h2>
+ <p><strong><a
+ id="glossAntecedent"></a>Antecedent</strong> (n.) In an <a
+ href="#glossInference" class="termref">inference</a>, the
+ expression(s) from which the <a href="#glossConsequent"
+ class="termref">conclusion</a> is derived. In an <a
+ href="#glossEntail" class="termref">entailment</a> relation, the
entailer. Also <em>assumption</em>.</p>
<p><strong><a id="glossAssertion"></a>Assertion</strong> (n.) (i) Any expression
@@ -1550,9 +1192,12 @@
be true.</p>
<p><strong><a id="glossClass"></a>Class</strong>
- (n.) A general concept, category or classification. Something<a class="termref" href="#glossResource"></a> used primarily to
- classify or categorize other things. Formally, in RDF, a <a class="termref" href="#glossResource">resource</a> of type
- <code>rdfs:Class</code> with an associated set of <a class="termref" href="#glossResource">resources</a> all of which
+ (n.) A general concept, category or classification. Something<a
+ href="#glossResource" class="termref"></a> used primarily to
+ classify or categorize other things. Formally, in RDF, a <a
+ href="#glossResource" class="termref">resource</a> of type
+ <code>rdfs:Class</code> with an associated set of <a
+ href="#glossResource" class="termref">resources</a> all of which
have the class as a value of the <code>rdf:type</code> property.
Classes are often called 'predicates' in the formal logical
literature.</p>
@@ -1560,10 +1205,15 @@
<p>(RDF distinguishes <em>class</em> from <em>set</em>, although the two are often
identified. Distinguishing classes from sets allows RDF more
freedom in constructing class hierarchies.</p>
-<p><strong><a id="glossComplete"></a>Complete</strong> (adj., of an inference system). (1)
- Able to detect all <a class="termref" href="#glossEntail">entailment</a>s between any two expressions.
- (2) Able to draw all <a class="termref" href="#glossValid">valid</a> inferences. See <a class="termref" href="#glossInference"><em>Inference</em></a>. Also used with a qualifier: able to
- detect entailments or draw all <a class="termref" href="#glossValid">valid</a> inferences in a certain limited form or kind (e.g.
+<p><strong><a
+ id="glossComplete"></a>Complete</strong> (adj., of an inference system). (1)
+ Able to detect all <a
+ href="#glossEntail" class="termref">entailment</a>s between any two expressions.
+ (2) Able to draw all <a href="#glossValid"
+ class="termref">valid</a> inferences. See <a href="#glossInference"
+ class="termref"><em>Inference</em></a>. Also used with a qualifier: able to
+ detect entailments or draw all <a href="#glossValid"
+ class="termref">valid</a> inferences in a certain limited form or kind (e.g.
between expressions in a certain normal form, or meeting certain syntactic conditions.)</p>
<p>(These definitions are not exactly equivalent, since the first requires that
the system has access to the consequent of the entailment, and may be unable
@@ -1571,13 +1221,18 @@
mechanical inference systems may be complete in the first sense but not necessarily
in the second.) </p>
- <p><strong><a id="glossConsequent"></a>Consequent</strong> (n.) In an inference,
- the expression constructed from the <a class="termref" href="#glossAntecedent">antecedent</a>. In an entailment relation, the
+ <p><strong><a
+ id="glossConsequent"></a>Consequent</strong> (n.) In an inference,
+ the expression constructed from the <a href="#glossAntecedent"
+ class="termref">antecedent</a>. In an entailment relation, the
entailee. Also <em>conclusion</em>.</p>
-<p><strong><a id="glossConsistent"></a>Consistent</strong> (adj., of an expression) Having
- a satisfying <a class="termref" href="#glossInterpretation">interpretation</a>; not internally contradictory. (Also used
+<p><strong><a
+ id="glossConsistent"></a>Consistent</strong> (adj., of an expression) Having
+ a satisfying <a href="#glossInterpretation"
+ class="termref">interpretation</a>; not internally contradictory. (Also used
of an inference system as synonym for <em>Correct</em>.) </p>
-<p><strong><a id="glossCorrect"></a>Correct</strong> (adj., of an inference system). Unable
+<p><strong><a
+ id="glossCorrect"></a>Correct</strong> (adj., of an inference system). Unable
to draw any invalid inferences, or unable to make false claims of entailment. See <em>Inference</em>.</p>
<p><strong><a id="glossDecidable"></a>Decidable</strong>
(adj., of an inference system). Able to determine for any pair of expressions,
@@ -1594,50 +1249,65 @@
expressions which holds whenever the truth of the first guarantees
the truth of the second. Equivalently, whenever it is logically
impossible for the first expression to be true and the second one
- false. Equivalently, when any <a class="termref" href="#glossInterpretation">interpretation</a> which <a class="termref" href="#glossSatisfy">satisfies</a> the first also satisfies the second.
+ false. Equivalently, when any <a href="#glossInterpretation"
+ class="termref">interpretation</a> which <a href="#glossSatisfy"
+ class="termref">satisfies</a> the first also satisfies the second.
(Also used between a set of expressions and an expression.)</p>
<p><strong><a id="glossEquivalent"></a>Equivalent</strong> (prep., with
<em>to</em>) True under exactly the same conditions; making
- identical claims about the world, when asserted. <a class="termref" href="#glossEntail">Entails</a> and is entailed
+ identical claims about the world, when asserted. <a
+ href="#glossEntail" class="termref">Entails</a> and is entailed
by.</p>
<p><strong><a id="glossExtensional"></a>Extensional</strong> (adj., of a logic) A
set-based theory or logic of classes, in which classes are
considered to be sets, properties considered to be sets of
<object, value> pairs, and so on. A theory which admits no
- distinction between entities with the same extension. See <a class="termref" href="#glossIntensional"><em>Intensional</em></a>.</p>
+ distinction between entities with the same extension. See <a
+ href="#glossIntensional"
+ class="termref"><em>Intensional</em></a>.</p>
- <p><strong><a id="glossFormal"></a>Formal</strong> (adj.) Couched in language
+ <p><strong><a
+ id="glossFormal"></a>Formal</strong> (adj.) Couched in language
sufficiently precise as to enable results to be established using
conventional mathematical techniques.</p>
<p><strong><a id="glossIff"></a>Iff</strong>
(conj.) Conventional abbreviation for 'if and only if'. Used to
express necessary and sufficient conditions.</p>
-<p><a id="glossInconsistent"></a><strong>Inconsistent</strong> (adj.) False under
- all interpretations; impossible to <a class="termref" href="#glossSatisfy">satisfy</a>. <strong>Inconsistency</strong>
+<p><a
+ id="glossInconsistent"></a><strong>Inconsistent</strong> (adj.) False under
+ all interpretations; impossible to <a
+ href="#glossSatisfy" class="termref">satisfy</a>. <strong>Inconsistency</strong>
(n.), any inconsistent expression or graph.</p>
-<p>(<a class="termref" href="#glossEntail">Entailment</a> and inconsistency are closely
+<p>(<a
+ href="#glossEntail" class="termref">Entailment</a> and inconsistency are closely
related, since A entails B just when (A and not-B) is inconsistent, c.f. the
- second definition for <a class="termref" href="#glossEntail">entailment</a>. This is the basis of many
+ second definition for <a
+ href="#glossEntail" class="termref">entailment</a>. This is the basis of many
mechanical inference systems. </p>
-<p>Although the definitions of <a class="termref" href="#glossConsistent">consistency</a>
+<p>Although the definitions of <a href="#glossConsistent" class="termref">consistency</a>
and inconsistency are exact duals, they are computationally dissimilar. It is
often harder to detect consistency in all cases than to detect inconsistency
- in all cases<a class="termref" href="#glossEntail"></a>.)</p>
-<p><strong><a id="glossIndexical"></a>Indexical</strong> (adj., of an expression) having
+ in all cases<a
+ href="#glossEntail" class="termref"></a>.)</p>
+<p><strong><a
+ id="glossIndexical"></a>Indexical</strong> (adj., of an expression) having
a meaning which implicitly refers to the context of use. Examples from English
include words like 'here', 'now', 'this'.</p>
-<p><strong><a id="glossInference"></a>Infer</strong><strong>ence</strong> (n.) An act or
+<p><strong><a
+ id="glossInference"></a>Infer</strong><strong>ence</strong> (n.) An act or
process of constructing new expressions from existing expressions, or the result
- of such an act or process. Inferences corresponding to <a class="termref" href="#glossEntail">entailments</a> are described as <em>correct</em> or <em>valid</em>.
+ of such an act or process. Inferences corresponding to <a href="#glossEntail"
+ class="termref">entailments</a> are described as <em>correct</em> or <em>valid</em>.
<strong>Inference rule</strong>, formal description of a type of inference;
<strong>inference system</strong>, organized system of inference rules; also,
software which generates inferences or checks inferences for validity.</p>
- <p><strong><a id="glossIntensional"></a>Intensional</strong> (adj., of a logic)
- Not <a class="termref" href="#glossExtensional">extensional</a>. A
+ <p><strong><a
+ id="glossIntensional"></a>Intensional</strong> (adj., of a logic)
+ Not <a href="#glossExtensional" class="termref">extensional</a>. A
logic which allows distinct entities with the same extension.</p>
@@ -1651,9 +1321,10 @@
have the same instances, such as human beings and bipedal hominids without body
hair. The semantics described in this document is basically intensional.)</p>
- <p><strong><a id="glossInterpretation"></a>Interpretation</strong>
+ <p><strong><a
+ id="glossInterpretation"></a>Interpretation</strong>
(<strong>of</strong>) (n.) A minimal formal description of those
- aspects of a <a class="termref" href="#glossWorld">world</a> which
+ aspects of a <a href="#glossWorld" class="termref">world</a> which
is just sufficient to establish the truth or falsity of any
expression of a logic.</p>
@@ -1665,35 +1336,44 @@
concept.)</p>
<p><strong><a id="glossLogic"></a>Logic</strong>
- (n.) A formal language which expresses <a class="termref" href="#glossProposition">propositions</a>.</p>
+ (n.) A formal language which expresses <a href="#glossProposition"
+ class="termref">propositions</a>.</p>
- <p><a id="glossMetaphysical"></a><strong>Metaphysical</strong> (adj.).
+ <p><a
+ id="glossMetaphysical"></a><strong>Metaphysical</strong> (adj.).
Concerned with the true nature of things in some absolute or
fundamental sense.</p>
- <p><a id="glossModeltheory"></a><strong>Model Theory</strong> (n.) A
+ <p><a
+ id="glossModeltheory"></a><strong>Model Theory</strong> (n.) A
formal semantic theory which relates expressions to
interpretations.</p>
<p>(The name 'model theory' arises from the usage, traditional in
logical semantics, in which a satisfying interpretation is called a
- "model". This usage is often found confusing, however, as it is
+ "model". This usage is often found confusing, however, as it is
almost exactly the inverse of the meaning implied by terms like
- "computational modelling", so has been avoided in this
+ "computational modelling", so has been avoided in this
document.)</p>
- <p><strong><a id="glossMonotonic"></a>Monotonic</strong> (adj., of a logic or
+ <p><strong><a
+ id="glossMonotonic"></a>Monotonic</strong> (adj., of a logic or
inference system) Satisfying the condition that if S entails E then
(S + T) entails E, i.e. adding information to some antecedents
- cannot invalidate a <a class="termref" href="#glossValid">valid</a> entailment.</p>
+ cannot invalidate a <a href="#glossValid"
+ class="termref">valid</a> entailment.</p>
- <p>(All logics based on a conventional <a class="termref" href="#glossModeltheory">model theory</a> and a standard notion of
+ <p>(All logics based on a conventional <a href="#glossModeltheory"
+ class="termref">model theory</a> and a standard notion of
entailment are monotonic. Monotonic logics have the property that
- entailments remain <a class="termref" href="#glossValid">valid</a> outside of the context in which they were
+ entailments remain <a href="#glossValid"
+ class="termref">valid</a> outside of the context in which they were
generated. This is why RDF is designed to be monotonic.)</p>
- <p><strong><a id="glossNonmonotonic"></a>Nonmonotonic</strong> (adj.,of a logic
- or inference system) Not <a class="termref" href="#glossMonotonic">monotonic</a>. Non-monotonic formalisms have been
+ <p><strong><a
+ id="glossNonmonotonic"></a>Nonmonotonic</strong> (adj.,of a logic
+ or inference system) Not <a href="#glossMonotonic"
+ class="termref">monotonic</a>. Non-monotonic formalisms have been
proposed and used in AI and various applications. Examples of
nonmonotonic inferences include <em>default reasoning</em>, where
one assumes a 'normal' general truth unless it is contradicted by
@@ -1713,17 +1393,20 @@
and providing explicit provenance information in the conclusion,
then closed-world reasoning is monotonic; it is the implicitness
that makes the reasoning nonmonotonic. Nonmonotonic conclusions can
- be said to be <a class="termref" href="#glossValid">valid</a> only in some kind of 'context', and are liable
+ be said to be <a href="#glossValid"
+ class="termref">valid</a> only in some kind of 'context', and are liable
to be incorrect or misleading when used outside that context.
Making the context explicit in the reasoning and visible in the
conclusion is a way to map them into a monotonic framework.)</p>
- <p><strong><a id="glossOntological"></a>Ontological</strong> (adj.) (Philosophy)
+ <p><strong><a
+ id="glossOntological"></a>Ontological</strong> (adj.) (Philosophy)
Concerned with what kinds of things really exist. (Applied)
Concerned with the details of a formal description of some topic or
domain.</p>
- <p><strong><a id="glossProposition"></a>Proposition</strong> (n.) Something that
+ <p><strong><a
+ id="glossProposition"></a>Proposition</strong> (n.) Something that
has a truth-value; a statement or expression that is true or
false.</p>
@@ -1738,31 +1421,38 @@
itself described using another syntax. In RDF, a reified triple is
a description of a triple-token using other RDF triples.</p>
- <p><strong><a id="glossResource"></a>Resource</strong> (n.)(as used in RDF)(i) An
+ <p><strong><a
+ id="glossResource"></a>Resource</strong> (n.)(as used in RDF)(i) An
entity; anything in the universe. (ii) As a class name: the class
of everything; the most inclusive category possible.</p>
- <p><strong><a id="glossSatisfy"></a>Satisfy</strong> (v.t.),
+ <p><strong><a
+ id="glossSatisfy"></a>Satisfy</strong> (v.t.),
<strong>satisfaction</strong>,(n.) <strong>satisfying</strong>
(adj., of an interpretation). To make true. The basic semantic
relationship between an interpretation and an expression. X
- satisfies Y means that if <a class="termref" href="#glossWorld">the
+ satisfies Y means that if <a href="#glossWorld" class="termref">the
world</a> conforms to the conditions described by X, then Y must be
true.</p>
- <p><strong><a id="glossSemantic"></a>Semantic</strong> (adj.) ,
+ <p><strong><a
+ id="glossSemantic"></a>Semantic</strong> (adj.) ,
<strong>semantics</strong> (n.). Concerned with the specification
of meanings. Often contrasted with <em>syntactic</em> to emphasize
the distinction between expressions and what they denote.</p>
- <p><a id="glossSkolemization"></a><a href="#skolemlemprf"><strong>Skolemization</strong></a> (n.) A
+ <p><a id="glossSkolemization"></a>
+<!-- <a href="#skolemlemprf"> -->
+<strong>Skolemization</strong></a> (n.) A
syntactic transformation in which blank nodes are replaced by 'new'
names.</p>
- <p>(Although not strictly <a class="termref" href="#glossValid">valid</a>, Skolemization retains the
+ <p>(Although not strictly <a href="#glossValid"
+ class="termref">valid</a>, Skolemization retains the
essential meaning of an expression and is often used in mechanical
inference systems. The full logical form is more complex. It is
- named after the logician <a href="http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html">
+ named after the logician <a
+ href="http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html">
A. T. Skolem</a>)</p>
<p><a id="glossToken"></a><strong>Token</strong>
@@ -1770,7 +1460,8 @@
a document. Usually contrasted with <em>type</em>, the abstract
grammatical form of an expression.</p>
- <p><strong><a id="glossUniverse"></a>Universe</strong> (n., also <em>Universe of
+ <p><strong><a
+ id="glossUniverse"></a>Universe</strong> (n., also <em>Universe of
discourse</em>) The universal classification, or the set of all
things that an interpretation considers to exist. In RDF/S, this is
identical to the set of resources.</p>
@@ -1780,35 +1471,39 @@
denote or refer to something else. The normal way that language is
used.</p>
- <p>("Whenever, in a sentence, we wish to say something about a
+ <p>("Whenever, in a sentence, we wish to say something about a
certain thing, we have to use, in this sentence, not the thing
- itself but its name or designation." - <a href="http://www.philosophypages.com/dy/t.htm">Alfred
+ itself but its name or designation." - <a
+ href="http://www.philosophypages.com/dy/t.htm">Alfred
Tarski</a>)</p>
<p><strong><a id="glossValid"></a>Valid</strong>
- (adj., of an inference or inference process) Corresponding to an <a class="termref" href="#glossEntail">entailment</a>, i.e. the
+ (adj., of an inference or inference process) Corresponding to an <a
+ href="#glossEntail" class="termref">entailment</a>, i.e. the
conclusion of the inference is entailed by the antecedent of the
inference. Also <em>correct</em>.</p>
- <p><dfn id="dfn-well-formed">Well-formed</dfn> (adj., of an
+ <p><dfn>Well-formed</dfn> (adj., of an
expression). Syntactically legal.</p>
<p><strong><a id="glossWorld"></a>World</strong>
(n.) (with <em>the:</em>) (i) The actual world. (with
<em>a:</em>) (ii) A way that the actual world might be arranged.
- (iii) An <a class="termref" href="#glossInterpretation">interpretation</a> (iv) A possible world.</p>
+ (iii) An <a href="#glossInterpretation"
+ class="termref">interpretation</a> (iv) A possible world.</p>
-<p>(The metaphysical status of '<a href="http://plato.stanford.edu/entries/actualism/possible-worlds.html">possible
+<p>(The metaphysical status of '<a
+ href="http://plato.stanford.edu/entries/actualism/possible-worlds.html">possible
worlds</a>' is highly controversial. Fortunately, one does not need to commit
oneself to a belief in parallel universes in order to use the concept in its
second and third senses, which are sufficient for semantic purposes.)</p>
-</div>
+</section>
- <div class="appendix section" id="acknowledgements">
- <h2><span class="secno">E </span>Acknowledgements</h2>
+ <section class='appendix'>
+ <h2 id="acknolwedgements">Acknowledgements</h2>
<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.</p>
@@ -1816,16 +1511,6 @@
<p>
Many thanks to Robin Berjon for making our lives so much easier with his cool tool. You betcha.
</p>
- </div>
-
-
-<div id="references" class="appendix section"><h2><span class="secno">F </span>References</h2><div id="normative-references" class="section"><h3><span class="secno">F.1 </span>Normative references</h3><dl class="bibliography"><dt id="bib-RDF-TESTCASES">[RDF-TESTCASES]</dt><dd>Jan Grant; Dave Beckett. <a href="http://www.w3.org/TR/2004/REC-rdf-testcases-20040210"><cite>RDF Test Cases.</cite></a> 10 February 2004. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2004/REC-rdf-testcases-20040210">http://www.w3.org/TR/2004/REC-rdf-testcases-20040210</a>
-</dd><dt id="bib-RDF11-CONCEPTS">[RDF11-CONCEPTS]</dt><dd>Richard Cyganiak; David Wood. <a href="http://www.w3.org/TR/2012/WD-rdf11-concepts-20120605/"><cite>RDF 1.1 Concepts and Abstract Syntax</cite></a> 05 June 2012. W3C Working Draft (work in progress). URL: <a href="http://www.w3.org/TR/2012/WD-rdf11-concepts-20120605/">http://www.w3.org/TR/2012/WD-rdf11-concepts-20120605/</a>
-</dd></dl></div><div id="informative-references" class="section"><h3><span class="secno">F.2 </span>Informative references</h3><dl class="bibliography"><dt id="bib-OWL2-OVERVIEW">[OWL2-OVERVIEW]</dt><dd>W3C OWL Working Group. <a href="http://www.w3.org/TR/2009/REC-owl2-overview-20091027/"><cite>OWL 2 Web Ontology Language: Overview.</cite></a> 27 October 2009. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2009/REC-owl2-overview-20091027/">http://www.w3.org/TR/2009/REC-owl2-overview-20091027/</a>
-</dd><dt id="bib-OWL2-SYNTAX">[OWL2-SYNTAX]</dt><dd>Boris Motik; Peter F. Patel-Schneider; Bijan Parsia. <a href="http://www.w3.org/TR/2009/REC-owl2-syntax-20091027/"><cite>OWL 2 Web Ontology Language:Structural Specification and Functional-Style Syntax.</cite></a> 27 October 2009. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2009/REC-owl2-syntax-20091027/">http://www.w3.org/TR/2009/REC-owl2-syntax-20091027/</a>
-</dd><dt id="bib-RDF-MT">[RDF-MT]</dt><dd>Patrick Hayes. <a href="http://www.w3.org/TR/2004/REC-rdf-mt-20040210"><cite>RDF Semantics.</cite></a> 10 February 2004. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2004/REC-rdf-mt-20040210">http://www.w3.org/TR/2004/REC-rdf-mt-20040210</a>
-</dd><dt id="bib-RDF-PRIMER">[RDF-PRIMER]</dt><dd>Frank Manola; Eric Miller. <a href="http://www.w3.org/TR/2004/REC-rdf-primer-20040210/"><cite>RDF Primer.</cite></a> 10 February 2004. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2004/REC-rdf-primer-20040210/">http://www.w3.org/TR/2004/REC-rdf-primer-20040210/</a>
-</dd><dt id="bib-RDF-SCHEMA">[RDF-SCHEMA]</dt><dd>Dan Brickley; Ramanathan V. Guha. <a href="http://www.w3.org/TR/2004/REC-rdf-schema-20040210"><cite>RDF Vocabulary Description Language 1.0: RDF Schema.</cite></a> 10 February 2004. W3C Recommendation. URL: <a href="http://www.w3.org/TR/2004/REC-rdf-schema-20040210">http://www.w3.org/TR/2004/REC-rdf-schema-20040210</a>
-</dd><dt id="bib-RIF-OVERVIEW">[RIF-OVERVIEW]</dt><dd>Michael Kifer; Harold Boley. <a href="http://www.w3.org/TR/2010/NOTE-rif-overview-20100622/"><cite>RIF Overview.</cite></a> 22 June 2010. W3C Working Group Note. URL: <a href="http://www.w3.org/TR/2010/NOTE-rif-overview-20100622/">http://www.w3.org/TR/2010/NOTE-rif-overview-20100622/</a>
-</dd><dt id="bib-TURTLE">[TURTLE]</dt><dd>David Beckett, Tim Berners-Lee. <a href="http://www.w3.org/TeamSubmission/turtle/"><cite>Turtle: Terse RDF Triple Language.</cite></a> January 2008. W3C Team Submission. URL: <a href="http://www.w3.org/TeamSubmission/turtle/">http://www.w3.org/TeamSubmission/turtle/</a>
-</dd></dl></div></div></body></html>
+ </section>
+ </body>
+</html>