**Mail folder:**Interlingua Mail**Next message:**sowa: "Re: Amendment to KIF's unary-relation and binary-relation"**Previous message:**macgregor@ISI.EDU: "Re: An ontology for KIF"**Reply:**sowa: "Re: Amendment to KIF's unary-relation and binary-relation"

Message-id: <199308252040.AA04880@quark.isi.edu> Date: Wed, 25 Aug 1993 13:39:27 -0800 To: interlingua@ISI.EDU From: macgregor@ISI.EDU Subject: Amendment to KIF's unary-relation and binary-relation

Apparently, I failed for some time to read some of the fine print in the KIF document, and I've only just discovered a new problem with it. The definitions of unary-relation and binary-relation include a "non-empty" clause, e.g., it is supposed to be impossible to define a non-empty unary-relation in KIF. This restriction needs to be remedied. The principal problem with the current document is that "unary-relation" and "binary-relation" as currently defined have unreasonably low applicability. Suppose I have a knowledge base consisting of the single statement (defrelation A (?a) :=> (Thing ?a)) (I am assuming that a top-level concept "Thing" is built-in to the system, but thats not really relevant). Is "A" a unary-relation? Well, we can't tell, since we have no axioms available asserting that A is not empty. That means among other things that we cannot confidently translate the definition of "A" into a Loom "defconcept" or to some other frame system's equivalent of "defclass". The current definition also means that we would be incautious if we were to incorporate "unary-relation" into a sugar-coated construct like Ontolingua's "define-class", i.e., the statement (define-class A (?a) :def (Thing ?a)) ought not to presume that instances that satisfy "A" necessarily exist (currently Ontolingua does presuppose the existence of members of its classes -- this is unfortunate). I propose that unary-relation and binary-relation be redefined in KIF as partial relations that DO NOT imply that their arguments are non-empty, i.e., define them as follows: (defrelation unary-relation (?r) :=> (forall (?l) (=> (member ?l ?r) (single ?l)))) (defrelation binary-relation (?r) :=> (forall (?l) (=> (member ?l ?r) (double ?l)))) With this redefinition, it is still the case that the bare definition (defrelation A (?a) :=> (Thing ?a)) cannot be interpreted as a definition of a concept A, but we can assume that an accompanying axiom (unary-relation A) would be generated by translators that translate concepts into KIF. Next, I would prefer that the property of being a unary- or binary-relation be considered analytic. However, this may not matter to KIF. Using the amended definition for "unary-relation" I can correctly translate the Loom statement (defconcept A :is-primitive Thing) into KIF as (defrelation A (?a) :=> (Thing ?a)) (defining-axiom 'A '(unary-relation A)) This raises a question about defining axioms. If a constant is bound to multiple defining axioms, is that equivalent to stating a single defining axiom that and's together all of the others? For example, are the two KIF statements just above equivalent to (defining-axiom 'A '(and (=> (member ?t A) (= (length ?t) 1)) (=> (A ?x) (Thing ?x)) (unary-relation A))) ? Cheers, Bob Robert M. MacGregor macgregor@isi.edu USC/ISI, 4676 Admiralty Way, Marina del Rey, CA 90292 (310) 822-1511