- From: pat hayes <phayes@ai.uwf.edu>
- Date: Mon, 2 Apr 2001 14:06:25 -0700
- To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
- Cc: kenb@ccs.neu.edu, www-rdf-logic@w3.org
>Ken may have pointed out a problem with the KIF axiomatization for >DAML+OIL. Yes. The issue of finite models is a delicate one for KIF itself, in fact. If KIF is taken to be a strict first-order language then there is no way to guarantee, on semantic grounds, that all lists are finite. The 'definition' of lists (also called 'sequences) in the extant KIF literature is a little vague on just this issue. (It uses sequence quantifiers, which Richard Fikes was careful to avoid in his axioms.) A working group is currently revising the KIF standard; the new version (a draft of which in the form of a working paper will be available soon) addresses this issue and provides a clear and unambiguous semantics for sequence quantifiers. With unrestricted usage of sequence quantification, KIF is a sublanguage of Lw1w, so is not first-order. In the meantime, one should probably think of 'lists' in the KIF axioms as referring to entities defined by a first-order theory, which therefore might include infinite lists (in fact, lists of any cardinality.) >However, even if we make the condition that properties have some local >finiteness built into them (and I'm not even sure if this does follow from >the KIF axiomatization, and it is certainly not in the model-theoretic >semantics), this does not mean that the entire domain is finite, nor does >it mean that a property (taken as a whole) need have a finite extension. Indeed. This issue is local to the definition of lists. Since these usages in the axiomatic spec. are restricted to data-structures, an alternative interpretation would assume that they are defined in the usual way as fixedpoints of recursive specifications, and that this specification is external to the model theory of the KIF axioms. Pat Hayes --------------------------------------------------------------------- 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 Monday, 2 April 2001 17:04:33 UTC