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Re: Strawman Model Theory

From: Dan Connolly <connolly@w3.org>
Date: Mon, 23 Jul 2001 02:36:41 -0500
Message-ID: <3B5BD409.3E97F31F@w3.org>
To: Brian McBride <bwm@hplb.hpl.hp.com>
CC: rdf core <w3c-rdfcore-wg@w3.org>
Brian McBride wrote:

Looks good, mostly...

> Here goes:
> Let U be the set of URI References (as defined by RDF 2396).

I don't think you mean that relative URI references
are in U. I think U is the set of absolute URI references;
i.e. URIs with optional #fragment thingies.

>                           //ignore lang and namespaces for now
> Let S be the set of of UNICODE strings (UNICODE*)
> An interpretation I consists of:
> A set R of thingies
> A subset P of thingies which corresponds to Properties
> A mapping IN : U -> R
> A mapping IEXT : P -> R x R            // R cross R
> A mapping IS : S -> R
> <s> <p> <o> .  is true in I if and only if:
>    s, o are members of U, p is a member of P
>    (IN(s), IN(o)) is a member of IEXT(I(P))

that last P should be little, no? IEXT(I(p))

> <s> <p> "string" . is true in I if and only if:
>    s is a member of U, p is a member of P and string is a member of S
>    (IN(s), IS(string)) is a member of IEXT(I(p))

Just 3 major things missing:

1. existentials:

	_:x <p> <o> is true in I iff
	o is a member of U, p is a member of P,
	and there is some thingy tx in I's set of thingies
	so that (tx, IN(O)) is a member of IEXT(I(p))

	The substitution (tx for _:x) is
	said to satisfy the triple _:x <p> <o>.

	In general, a substitution has
	any number of (thingy for _:name, thingy2 for _:name2, ...)

2. conjunctions

	a list of triples is satisfied by
	some substitution if each of the triples
	in it is satisfied by that substitution.

3. putting it all together

	A list of triples is true in I iff there's some
	substitution that satisfies it.

> Pat goes on to demonstrate a use of this base model theory to
> define the meaning of reification:
> Pat points out an issue with reification, and I have another,
> but I suggest we get the base model theory sorted out before we get
> into that.

Yes, let's leave that for a rainy day...

Just one of Pat's notes seems essential:

> (Literals are required by law
> to map to a certain subset of thingies in a predefined way, but
> otherwise are treated like any other names.)

I'd say literals map to themselves. i.e. IS is the
identity function.

But that depends on my position on xml:lang...

Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Monday, 23 July 2001 03:38:06 UTC

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