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Re: Infinite cardinalities

From: Richard Fikes <fikes@KSL.Stanford.EDU>
Date: Mon, 02 Apr 2001 16:39:59 -0700
Message-ID: <3AC90DCF.E25D3BAB@ksl.stanford.edu>
To: pat hayes <phayes@ai.uwf.edu>
CC: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, kenb@ccs.neu.edu, www-rdf-logic@w3.org
> 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.

Chapter 8 of the "draft proposed American National Standard (dpANS)" of
KIF (at http://logic.stanford.edu/kif/dpans.html) says that a list is a
finite sequence of objects.  The formal definition of a list (attached
below) given in that chapter uses a sequence variable, as you say.  The
model theoretics document for KIF (at
http://logic.stanford.edu/kif/semantics.tex) says that a variable
assignment maps a sequence variable into a finite sequence of objects. 
So, the prose in chapter 8 and the prose in the semantics document are
consistent in saying that lists are finite.

> 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.

I expect the new standard document will indeed clarify many such issues.

Richard

----------------------------------------------

>     (defrelation list (?x) :=
>       (exists (@l) (= ?x (listof @l))))
Received on Monday, 2 April 2001 19:40:45 GMT

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