--- a/rdf-mt/index.html Thu Mar 07 10:53:36 2013 -0600
+++ b/rdf-mt/index.html Thu Mar 07 12:07:25 2013 -0600
@@ -574,7 +574,11 @@
<p><a id="DefSemanticExtension" name="DefSemanticExtension"></a>RDF is intended for use as a base notation for a variety of extended notations such as OWL //ref// and RIF //ref//, whose expressions can be encoded as RDF graphs which use a particular vocabulary with a specially defined meaning. In addition, 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 an <em>RDF semantic extension</em>. Each semantic extension defines an <em>entailment regime</em> 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 rdfs-entailment, owl-entailment. All entailment regimes <strong class="RFC2119">MUST</strong> be <em>monotonic</em> extensions of the simple entailment regime described in the next section, in the sense that if A simply entails B then A must also entail B under any extended notion of entailment. Put another way, a semantic extension cannot "cancel" an entailment made by a weaker entailment regime.</p>
+<p>A particular such set of semantic assumptions is called an <em>RDF semantic extension</em>. Each semantic extension defines an <em>entailment regime</em> 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>owl-entailment</em>, etc.. </p>
+
+<p>Semantic extensions <strong class="RFC2119">MAY</strong> 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 <strong class="RFC2119">MAY</strong> consider RDF graphs which do not conform to these conditions to be syntax errors. ///Give OWL-DLexample///. 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.</p><p> None of the semantic extensions normatively defined in this document impose syntactic restrictions on RDF graphs.</p>
+
+<p>All entailment regimes <strong class="RFC2119">MUST</strong> be <em>monotonic</em> extensions of the simple entailment regime described in the next section, in the sense that if A simply entails B then A must also entail 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>
<h1>Notation and terminology</h1>
@@ -606,6 +610,69 @@
<p>A <em>name</em> is any IRI or literal. A <em>vocabulary</em> is a set of names.
</p>
+<p class="issue">This rest of this section is lifted almost verbatim from the 2004 document. Some of these definitions may not be needed. This will be cleaned up in a final edit.<br/><br/>
+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?.
+
+<p><a name="defgraph" id="defgraph">An <span > <a href="http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/#dfn-rdf-graph"><em>RDF
+ graph</em></a></span>, or simply a <em>graph</em>, is a set of RDF triples.</a></p>
+<p><a name="defsubg" id="defsubg">A <i>subgraph</i> of an RDF graph is a subset
+ of the triples in the graph.</a> A triple is identified with the singleton set
+ containing it, so that each triple in a graph is considered to be a subgraph.
+ A <em>proper</em> subgraph is a proper subset of the triples in the graph. </p>
+
+
+<p><a name="defgd" id="defgd">A <em>ground</em> RDF graph is one with no blank
+ nodes.</a></p>
+
+
+<p><a name="defname" id="defname">A <em>name</em> is an IRI or a literal.</a>
+ Note that a typed literal comprises
+ two <a href="#defname" class="termref">name</a>s: itself and its internal type
+ IRI. </p>
+<p><a name="defvocab" id="defvocab"></a> A set of <a href="#defname" class="termref">name</a>s
+ is referred to as a <i>vocabulary</i>. The vocabulary <em>of</em> 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><a name="definst" id="definst"> 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 <em>instance</em> of G.</a> 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 some triple
+ in G.</p>
+<p><a name="definstvoc" id="definstvoc">An instance <i>with respect to a vocabulary</i>
+ V </a>is an <a href="#definst" class="termref">instance</a> in which all the
+ <a href="#defname" class="termref">name</a>s in the instance that were substituted
+ for blank nodes in the original are <a href="#defname" class="termref">name</a>s
+ from V.</p>
+<p><a name="defpropinst" id="defpropinst">A <i>proper</i> instance</a> of a graph
+ is an instance 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 instance 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 <a href="http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/#section-graph-equality">equivalent</a>.
+ We will often treat such equivalent graphs as identical. Equivalent graphs are mutual instances with an invertible instance
+ mapping.</p>
+<p ><span ><a id="deflean"
+ name="deflean">An RDF graph is <em>lean</em> if it has no instance which is
+ a proper subgraph of the graph.</a> Non-lean graphs have internal redundancy
+ and express the same content as their lean subgraphs. For example, the graph</span></p>
+<p ><code><ex:a> <ex:p> _:x .<br />
+ _:y <ex:p> _:x .</code></p>
+<p >is not <a
+ href="#deflean" class="termref">lean</a>, but</p>
+<p ><code><ex:a> <ex:p> _:x .<br />
+ _:x <ex:p> _:x .</code></p>
+<p >is <a
+ href="#deflean" class="termref">lean</a>. </p>
+
+
+
<h2><a id="sinterp" name="sinterp"> Simple Interpretations</a> </h2>
@@ -734,70 +801,6 @@
<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 //ref// 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><a name="graphdefs" id="graphdefs">Graph Definitions </h3>
-
-<p class="issue">This section is lifted almost verbatim from the 2004 document. Some of these definitions may not be needed. This will be cleaned up in a final edit.<br/><br/>
-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?.
-
-
-<p><a name="defgraph" id="defgraph">An <span > <a href="http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/#dfn-rdf-graph"><em>RDF
- graph</em></a></span>, or simply a <em>graph</em>, is a set of RDF triples.</a></p>
-<p><a name="defsubg" id="defsubg">A <i>subgraph</i> of an RDF graph is a subset
- of the triples in the graph.</a> A triple is identified with the singleton set
- containing it, so that each triple in a graph is considered to be a subgraph.
- A <em>proper</em> subgraph is a proper subset of the triples in the graph. </p>
-
-
-<p><a name="defgd" id="defgd">A <em>ground</em> RDF graph is one with no blank
- nodes.</a></p>
-
-
-<p><a name="defname" id="defname">A <em>name</em> is an IRI or a literal.</a>
- Note that a typed literal comprises
- two <a href="#defname" class="termref">name</a>s: itself and its internal type
- IRI. </p>
-<p><a name="defvocab" id="defvocab"></a> A set of <a href="#defname" class="termref">name</a>s
- is referred to as a <i>vocabulary</i>. The vocabulary <em>of</em> 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><a name="definst" id="definst"> 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 <em>instance</em> of G.</a> 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 some triple
- in G.</p>
-<p><a name="definstvoc" id="definstvoc">An instance <i>with respect to a vocabulary</i>
- V </a>is an <a href="#definst" class="termref">instance</a> in which all the
- <a href="#defname" class="termref">name</a>s in the instance that were substituted
- for blank nodes in the original are <a href="#defname" class="termref">name</a>s
- from V.</p>
-<p><a name="defpropinst" id="defpropinst">A <i>proper</i> instance</a> of a graph
- is an instance 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 instance 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 <a href="http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/#section-graph-equality">equivalent</a>.
- We will often treat such equivalent graphs as identical. Equivalent graphs are mutual instances with an invertible instance
- mapping.</p>
-<p ><span ><a id="deflean"
- name="deflean">An RDF graph is <em>lean</em> if it has no instance which is
- a proper subgraph of the graph.</a> Non-lean graphs have internal redundancy
- and express the same content as their lean subgraphs. For example, the graph</span></p>
-<p ><code><ex:a> <ex:p> _:x .<br />
- _:y <ex:p> _:x .</code></p>
-<p >is not <a
- href="#deflean" class="termref">lean</a>, but</p>
-<p ><code><ex:a> <ex:p> _:x .<br />
- _:x <ex:p> _:x .</code></p>
-<p >is <a
- href="#deflean" class="termref">lean</a>. </p>
-
<h3>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