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Re: Model Theory, sets of statements and anon resources

From: Graham Klyne <Graham.Klyne@Baltimore.com>
Date: Mon, 23 Jul 2001 22:34:31 +0100
Message-Id: <5.1.0.14.2.20010723221921.03bc5890@joy.songbird.com>
To: Brian McBride <bwm@hplb.hpl.hp.com>
Cc: rdf core <w3c-rdfcore-wg@w3.org>
At 08:03 AM 7/23/01 +0100, Brian McBride wrote:
>The model theory defines an interpretation for a single statement.  We also
>need to formally deal with sets of statements i.e.
>
>{s1, s2, ..., sn} is true under an interpetation I if and only if each si
>is true under I.
>
>Depending on our decision about anonymous resources we may also need
>an interpretation statments containing them.  Only the subject case
>is shown here - the others are similar:
>
>_:a <p> <o> . is true under an interpretation I if and only if
>
>   p and o are members of U and
>   there exists ?a such that ?a is a member of R and
>                             (?a, IN(o)) is a member of IEXT(I(p))
>
>And finally (I don't know how to say this formally) the scope of
>the names of the form _:name is a set of statements.

Concerning "and finally"...

I think what Pat hinted at in the last teleconference was that certain 
special identifiers (e.g. of the form _:name) might be global to the scope 
of any given set of statements, but that if two such sets were brought 
together then such identifiers would be rewritten to avoid conflicts, thus 
ensuring uniqueness in the new, combined set.

(It's similar to the renaming of free variables that is required when 
evaluating lambda expressions where an argument to a function contains free 
variable names that are also bound within the function body.)

Thus, the special handling of "variables" takes the form of a syntactic 
manipulation when statement sets are brought together.  Otherwise, they 
behave just like the other identifiers - URIs.

#g


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Graham Klyne                    Baltimore Technologies
Strategic Research              Content Security Group
<Graham.Klyne@Baltimore.com>    <http://www.mimesweeper.com>
                                 <http://www.baltimore.com>
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Received on Monday, 23 July 2001 18:05:37 EDT

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