--- a/rdf-mt/index.html Wed Jun 19 12:25:18 2013 -0400
+++ b/rdf-mt/index.html Wed Jun 19 12:22:34 2013 -0500
@@ -176,7 +176,7 @@
<p>A particular such set of semantic assumptions is called a <dfn>semantic extension</dfn>. Each <a>semantic extension</a> defines an <dfn>entailment regime</dfn> of entailments which are valid under that extension. RDFS, described later in this document, is one such <a>semantic extension</a>. We will refer to an entailment regime by names such as <em> RDFS entailment</em>, <em>D-entailment</em>, etc. </p>
-<p><a>Semantic extension</a>s 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/><br/> <code>ex:a rdfs:subClassOf "Thing"^^xsd:string .</code><br/><br/> are prohibited in the OWL <a>semantic extension</a> based on description logics [[[OWL2-SYNTAX]]. 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 <a>semantic extension</a>s normatively defined in this document impose such syntactic restrictions on RDF graphs.</p>
+<p><a>Semantic extension</a>s 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/><br/> <code>ex:a rdfs:subClassOf "Thing"^^xsd:string .</code><br/><br/> are prohibited in the OWL <a>semantic extension</a> based on description logics [[!OWL2-SYNTAX]]. In such cases, basic RDF operations such as taking a subset of triples, or combining RDF graphs, may cause syntax errors in parsers which recognize the extension conditions. None of the <a>semantic extension</a>s normatively defined in this document impose such syntactic restrictions on RDF graphs.</p>
<p>All entailment regimes MUST be <a>monotonic</a> extensions of the simple entailment regime described in the document, in the sense that if A <a>simply entails</a> B then A also entails B under any extended notion of entailment, provided that any syntactic conditions of the extension are also satisfied. Put another way, a <a>semantic extension</a> cannot "cancel" an entailment made by a weaker entailment regime, although it can treat the result as a syntax error.</p>
</section>
@@ -281,6 +281,8 @@
<p>The union is always an instance of the merge. If graphs have no blank nodes in common, then their merge and union are identical. </p>
+<p>If S is a set of graphs, then the set obtained by replacing any subsets of S which share a blank node by their union, is the <dfn>unionizing</dfn> of S. If no graphs in S share any blank nodes, then the unionizing of S is the same as S. The unionizing of S accurately represents the combined meaning of the graphs in S. </p>
+
</section>
</section>
@@ -400,6 +402,8 @@
<p> and an interpretation I over the universe {Alice, Bob, Monica, Ruth} with:<br/>
I(<code>ex:Alice</code>)=Alice, I(<code>ex:Bob</code>)=Bob, IEXT(I(<code>ex:hasChild</code>))={<Alice,Monica>,<Bob,Ruth> }<br/></p>
<p>Each of the inner graphs is true under this interpretation, but the two of them together is not, because the three-node graph says that Alice and Bob have a child together. In order to capture the full meaning of graphs sharing a blank node, it is necessary to consider the union graph containing all the triples which contain the blank node.</p>
+<p class="technote"> RDF graphs can be viewed as conjunctions of simple atomic sentences in first-order logic, where blank nodes are free variables which are understood to be existential. Taking the union of two graphs is then analogous to syntactic conjunction in this syntax. RDF syntax has no explicit variable-binding quantifiers, so the truth conditions for any RDF graph treat the free variables in that graph as existentially quantified in that graph. Taking the union of graphs which share a blank node changes the implied quantifier scopes. The unionizing of a set of graphs accurately reflects the smallest quantifier scopes which capture the full meaning of the graphs in the set.
+</p>
</section>
@@ -414,7 +418,7 @@
<section id="simpleentailment"><h2>Simple Entailment</h2>
-<p>Following standard terminology, we say that I <dfn>satisfies</dfn> E when I(E)=true, that E is <dfn>satisfiable</dfn> when an interpretation exists which satisfies it, (otherwise <dfn>unsatisfiable</dfn>), that a graph G <dfn>simply entails</dfn> a graph E when every interpretation which satisfies G also satisfies E, and that a set S of graphs simply entails E when the union of S simply entails E. 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>Following standard terminology, we say that I <dfn>satisfies</dfn> E when I(E)=true, that E is <dfn>satisfiable</dfn> when an interpretation exists which satisfies it, (otherwise <dfn>unsatisfiable</dfn>), that a graph G <dfn>simply entails</dfn> a graph E when every interpretation which satisfies G also satisfies E. If S is a set of graphs then S simply entails E when the <a>unionizing</a> of S simply entails E. In later sections these notions will be adapted to other classes of interpretations, but throughout this section 'entailment' should be interpreted as meaning simple entailment.
</p>
<p class="changenote">This definition treats a set of graphs identically to its union, unlike the definition used in the 2004 RDF 1.0 Semantics. This is more appropriate for the case where graphs may share blank nodes, as can occur with the graphs in an RDF dataset. If this case does not arise, this definition is exactly equivalent to the previous definition.</p>