Re: SUO: RE: Re: More KIF-ified Ontology Content
>----- Original Message -----
>From: "pat hayes" <phayes@ai.uwf.edu>
>To: "West, Matthew MR SSI-GREA-UK" <Matthew.R.West@IS.shell.com>
>Cc: <standard-upper-ontology@majordomo.ieee.org>
>Sent: Thursday, February 08, 2001 5:59 PM
>Subject: RE: SUO: RE: Re: More KIF-ified Ontology Content
>
>
><snip>
>
> > Yes, I entirely agree. In fact there is a way to transcribe all of
> > Hobbs' axioms and schemas (he has all this stuff worked out in
> > enormous detail) into a slightly odd version of FOL (one that ought
> > to appeal to Jon Awbry) in which every open sentence can be seen as a
> > relation name (so you can write things like
> > (R & Q)(a,b) to mean R(a,b) & Q(a,b) ), and all the 'things' in
> > Hobbs' ontology become ways of talking about the things you or I
> > would think were really there. (The cute part of this mapping is that
> > one gets *exactly* the same conclusions, somewhat undercutting the
> > ontological claims being made. Sorry, couldn't help a bit of public
> > gloating there.)
>
>I don't know why this would appeal to Jon Awbry, but I question why it is
>seen as a slightly odd version of FOL. The idea that "every open sentence
>can be seen as a relation name" seems quite natural,
Yes, I agree it is natural (and an old idea), and to category theory
folk it is like breathing, but it isn't part of the usual syntactic
or inferential rules of FOL, is all I meant: it is much more like
higher-order logic (HOL) than first-order.
The revised KIF coming shortly will move a small step in this
direction but by no means all the way.
>and appears in my
>category-theory approach -- starting with any (type) language L one can
>generate an associated, and more inclusive, type language expr(L) whose
>relation names consist of all open L-sentences. You don't even need to write
>explicitly '(R & Q)(a,b)'; just use 'R(a,b) & Q(a,b)' itself.
Yes: in a type-theoretic version of HOL they could both be more
properly written as (lambda (x y) (R(x, y) & Q(x, y))) (a,b). This is
why I thought Jon Awbrey would like it, since everything is a
function, just as he thinks it should be. Even the propositional
connectives like AND, and even quantifiers, can be seen as functions.
>What is
>precisely meant by your statement that "one gets exactly the same
>conclusions"?.
Sorry, I meant that this transcription of Hobbs' ontology preserves
all the conclusions he is able to draw (under transliteration).
Never mind, it would take too long to explain it and its not really
important, other than being another little nugget in the
overwhelmingly large pile of evidence suggesting that extensional FOL
is the ontology language of choice.
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