Re: entailment on sets of RDF graphs (union vs merge semantics)

OK, I have put all these into the latest edit. Thanks, you caught some I missed (and vice versa :-)

Pat

On Jun 20, 2013, at 12:59 AM, Peter F. Patel-Schneider wrote:

> Here are the changes (plus a fix to finite interpretations).   I didn't find any substantive changes, and the changes were not substantial after all.  By far the biggest differences are in the first two modifications, everything else amounts to eliminating sets of graphs on the LHS of entailment.
> 
> If everyone is happy with these, I'll update the document.
> 
> peter
> 
> REMOVED
> If S is a set of graphs then S simply entails E when any every
> interpretation which satisfies every member of the <a>unionizing</a> of S
> also satisfies E.
> /REMOVED

And the definition of unionizing, which is now redundant. I mean, why not just take the bloody union. 

> 
> CHANGED
> <p class="changenote"> Before determining whether a set of graphs entails
> another graph, which was directly defined in the 2004 RDF 1.0 Semantics, the
> graphs have to first be unionized or merged (if there is some reason to
> treat shared blank nodes as if they were different in different graphs).
> If there are no shared blank nodes unioning and merging produce the same
> result, which is the also the same as the direct 2004 definition. </p>
> 
>    <p><a id="defvalid">Any process which constructs a graph E from
>    some other graph S is (simply) <dfn>valid</dfn> if S
>    simply entails E in every case, otherwise <dfn>invalid.</dfn></a></p>
> /CHANGED
> 
> 
> CHANGED
> <p> completely characterizes simple entailment in syntactic
>  terms. To detect whether an RDF graph simply entails another, check that
>  there is some instance of the entailed graph which is a subset of the
> entailing graph. </p>
> /CHANGED
> 
> CHANGED
> <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 makes S true also D-satisfies
> G.</p>
> /CHANGED
> 
> CHANGED
> In all these cases, a pre-interpretation of the vocabulary of a graph may be
> extended to a full interpretation of the appropriate type without changing
> the truth-values of any triples in the graph.</p>
> /CHANGED
> 
> CHANGED for other reasons
> <p>Basically, it is only necessary for an interpretation structure to
> interpret the <a>name</a>s actually used in the graphs whose entailment is
> being considered, and to consider interpretations whose universes are at
> most as big as the number of names and blank nodes in the graphs. More
> formally, we can define a <dfn>pre-interpretation</dfn> over a
> <a>vocabulary</a> V to be a structure I similar to a <a>simple
> interpretation</a> but with a mapping only from V to its universe IR.  Then
> when determining whether G entails E, consider only pre-interpretations over
> the finite vocabulary of <a>name</a>s actually used in G union E. The
> universe of such a pre-interpretation can be restricted to the cardinality
> N+B***+1***, where N is the size of the vocabulary and B is the number of
> blank nodes in the graphs. Any such pre-interpretation may be extended to
> <a>simple interpretation</a>s, all of which will give the same truth values
> for any triples in G or E. Satisfiability, entailment and so on can then be
> defined with respect to these finite pre-interpretations, and shown to be
> identical to the ideas defined in the body of the specification.</p>
> /CHANGED
> 
> 

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Received on Friday, 21 June 2013 03:34:33 UTC