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Re: RDF Abstract Syntax: a strawman

From: pat hayes <phayes@ai.uwf.edu>
Date: Wed, 30 May 2001 10:26:26 -0500
Message-Id: <v04210102b73abe99381c@[205.160.76.176]>
To: Jerome.Euzenat@inrialpes.fr (Je'ro^me Euzenat)
Cc: www-rdf-logic@w3.org
>Hello,
>
>In his message (Re: RDF Abstract Syntax: a strawman) of 29/05/01,
>pat hayes wrote:
>>>  % hmm... are predicates
>>>  % limited to constants?
>>>  % The RDF 1.0 syntax suggests
>>>  % so, but n3 doesn't have that
>>>  % restriction
>>
>>It is conventional to so limit them, but we relaxed this in the new 
>>KIF without apparently causing enormous problems. When there are 
>>predicate variables it is difficult to prevent things like applying 
>>a predicate to itself (more generally, any 'loop' of applications, 
>>eg applying P to Q and Q to P) which breaks the 'standard' 
>>first-order model theory , but Chris Menzel invented a neat way to 
>>repair it without causing much harm, or one can be even braver and 
>>use a nonstandard set theory to do the semantics with. So in sum: 
>>go ahead and allow variables in predicate position, and if anyone 
>>accuses you of doing higher-order logic, send them to me.
>
>Here I am.

OK. In brief: FOL model theory says that the universe of 
quantification is a set. It does not say that the set cannot contain 
relations. So quantifying over relations is not ruled out by FOL. 
What makes a language higher-order is when its relational quantifiers 
are required to range over a rather large set of relations (exactly 
how large depends on the logic, eg classical HOL= *all* relations, ie 
the set 2|(D|n) where D is the base domain of individuals; Henkin 
logic = all lambda-definable relations.) If one does not impose any 
requirement on the size of the relational universe (other than it 
provide a denotation for every relational term) then there is nothing 
higher-order in the semantics and it is easy to allow quantification 
over relations and still be first-order. Those quantifiers have only 
a first-order kind of 'bite', of course, and the language has no 
rules of lambda-conversion.

>any reference to that Chris Menzel stuff? (google does not know that 
>guy, is he classified?)

My google got him first hit: http://philebus.tamu.edu/~cmenzel/. The 
stuff is in a paper, see
  http://philebus.tamu.edu/~cmenzel/Papers/HayesMenzel-SKIF-IJCAI2001.pdf.

Pat

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Received on Wednesday, 30 May 2001 11:26:36 UTC

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