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Model theory ideas for TDL

From: Graham Klyne <GK@NineByNine.org>
Date: Wed, 30 Jan 2002 16:00:36 +0000
Message-Id: <5.1.0.14.2.20020130154904.037b2290@joy.songbird.com>
To: www-archive@w3.org
[From a comment to Jeremy Carroll about a model theoretic formulation for 
the TDL proposal for datatyping in RDF.]

For background, see also:
http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2002Jan/0344.html
http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2002Jan/0369.html
http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2002Jan/0384.html
http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2002Jan/0353.html
http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2002Jan/0349.html
(and other messages in that thread.)

Also, a thread starting with:
http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2002Jan/0224.html

-----

I have an inkling that a model theory that treated all literals 
existentially, without introducing extra nodes, might just work for 
TDL.  Sketch:

(a) Literals denote <value,string> pairs as previously noted.

(b) Interpretation (of statements containing literals) is with respect to a 
defined set of data types DT, where each d in DT is a set of pairs of the 
form <value,string> -- i.e. a datatype map.  (DT would be a subset of IC, 
mapped to a subset of IC, I think.)

(c) a triple I(aaa bbb "foo") is true if there exists a value v such that 
<v,"foo"> is in the union of the members of DT, and <I(aaa),v> is in 
IEXT(I(bbb)).

Roughly, the statement is true if there exists any datatype mapping that 
makes it true.  If the set DT is required to contain the identity mapping 
of strings (dstring: (<x,x>:for all strings x that can be used as literal 
node labels>), then I think the self-entailment of documents containing 
literals follows.

This is all intuitive;  I'm not sure I could prove it.



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Received on Wednesday, 30 January 2002 11:00:51 GMT

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