# 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>

```[From a comment to Jeremy Carroll about a model theoretic formulation for
the TDL proposal for datatyping in RDF.]

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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/\ \    Graham Klyne
/  \ \   (GK@ACM.ORG)
/ /\ \ \
/ / /\ \ \
/ / /__\_\ \
/ / /________\
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```
Received on Wednesday, 30 January 2002 11:00:51 GMT

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