author Pat Hayes Thu, 20 Jun 2013 01:54:03 -0500 changeset 861 99f024c81d42 parent 860 9cb14ea07161 child 862 f46f2a58ee82
Minor bugs in previous edit now fixed
 rdf-mt/index.html
```--- a/rdf-mt/index.html	Thu Jun 20 01:43:04 2013 -0500
+++ b/rdf-mt/index.html	Thu Jun 20 01:54:03 2013 -0500
@@ -449,9 +449,8 @@
</p>

<p> completely characterizes simple entailment in syntactic
-  terms. To detect 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 union
-  of the original set of graphs. </p>
+  terms. To detect whether one RDF graph simply entails another, check that
+  there is some instance of the entailed graph which is a subset of the first graph. </p>

<p class="technote">This is clearly decidable, but it is also difficult to determine in general, since one can encode the NP-hard subgraph problem (detecting whether one mathematical graph is a subgraph of another) as detecting simple entailment between RDF graphs. This construction (due to Jeremy Carroll) uses graphs containing many blank nodes, which are unlikely to occur in practice. The complexity of checking simple entailment is reduced by having fewer blank nodes in the conclusion E. When E is a <a>ground</a> graph, it is simply a matter of checking the subset relationship on sets of triples.</p>

@@ -549,7 +548,7 @@
<section>
<h3 id="D_entailment">Datatype entailment</h3>

-<p>A graph is (simply) <dfn>D-satisfiable</dfn> or <dfn>satisfiable recognizing D</dfn> when it has the value true in some D-interpretation, and a set S of graphs (simply) <dfn>D-entails</dfn> or <dfn>entails recognizing D</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> or <dfn>satisfiable recognizing D</dfn> when it has the value true in some D-interpretation, and a graph S (simply) <dfn>D-entails</dfn> or <dfn>entails recognizing D</dfn> a graph G when every D-interpretation which satisfies S also D-satisfies G.</p>

<p> Unlike the case with <a>simple interpretation</a>s, it is possible for a graph to have no satisfying D-interpretations, i.e. to be <dfn>D-unsatisfiable</dfn>. RDF processors MAY treat an unsatisfiable graph as signaling an error condition, but this is not required.</p>
```