- From: Stefan Decker <stefan@db.stanford.edu>
- Date: Wed, 30 May 2001 11:53:10 -0700
- To: Jerome.Euzenat@inrialpes.fr (Je'ro^me Euzenat)
- Cc: www-rdf-logic@w3.org
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 > >--------------------------------------------------------------------- >IHMC (850)434 8903 home >40 South Alcaniz St. (850)202 4416 office >Pensacola, FL 32501 (850)202 4440 fax >phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes
Received on Wednesday, 30 May 2001 14:52:57 UTC