# Re: RDF Abstract Syntax: a strawman

From: Stefan Decker <stefan@db.stanford.edu>
Date: Wed, 30 May 2001 11:53:10 -0700
Message-Id: <5.0.2.1.2.20010530114320.034a4a38@db.stanford.edu>
To: Jerome.Euzenat@inrialpes.fr (Je'ro^me Euzenat)

```Jerome,

another paper discussing the principles and an implementation of
second order syntax with first order semantics for logic programing is:

HiLog: A Foundation for Higher-Order Logic Programming (1989)
Weidong Chen Michael Kifer David S. Warren
The Journal of Logic Programming
http://citeseer.nj.nec.com/chen89hilog.html

The implementation trick is simple:

atoms like p(X) are compiled into
unaryPred(p,X).

the same predicate unaryPred is used for all predicates in the original
language
with arity 1 and so forth.

All the best,

Stefan

At 10:26 AM 5/30/2001 -0500, pat hayes wrote:
>>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 14:52:57 UTC

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