RE: SUO: Where are the axioms that establish the condition of a class ?
Seth,
See my comment below.
-Ian
> -----Original Message-----
> From: Seth Russell [mailto:seth@robustai.net]
> Sent: Tuesday, January 15, 2002 2:03 PM
> To: Ian Niles; standard-upper-ontology@ieee.org
> Subject: Re: SUO: Where are the axioms that establish the
> condition of a
> class ?
>
>
> From: "Ian Niles" <iniles@teknowledge.com>
>
> > I don't think you're proposed "criteria" definition has any
> advantages
> over
> > this representation.
>
> The only tangible advantage is that the KappaFn is to be
> depreciated and has
> no axiomatic definition .. so if we don't define the KappaFn
> and depreciate
> it, then we will loose this ability.
It's true that 'KappaFn' has no axioms and is deprecated. It is deprecated,
because in most cases it is possible to create a complex class by means of
the class-forming operators that don't give rise to Russell's Paradox, e.g.
'UnionFn', 'IntersectionFn', 'ComplementFn', etc. Although 'KappaFn' has no
defining axiom, your proposed predicate "criteria" fares little better in
comparison.
(<=>
(criteria ?CLASS ?FORMULA)
( (exists ?FORMULA ?X)
(<=>
(equal ?FORMULA True)
(instance ?X ?CLASS)
First of all, the axiom isn't true, because not every formula specifying the
intension of a class is true. For example, the intension of the class of
unicorns is going to be something like 'an omnivorous quadruped with a horn
sticking out of its forehead', and the formula specifying this intension
will either be false or lack a truth value. Thus, the axiom should say just
that the first argument of "criteria" is a 'Class' and the second argument
is a 'Formula'. However, these are just argument-type restrictions, and, in
fact, 'KappaFn' has similiar such restrictions. Thus, in sum, I don't see
that "criteria" has any advantages over 'KappaFn' (and the other
class-forming operators defined in the SUMO).
>I have some other
> personal reasons
> why a binary relation that doesn't involve the use of the
> term 'equal' would
> be more advantageous; but I doubt those would mean much to
> the rest of you
> all.
>
> Seth Russell
>
>