RE: SUO: Where are the axioms that establish the condition of a class ?
Seth,
See my comments below.
-Ian
> -----Original Message-----
> From: Seth Russell [mailto:seth@robustai.net]
> Sent: Friday, January 18, 2002 8:37 AM
> 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>
>
> > It's true that 'KappaFn' has no axioms and is [depreciated]. It is
> [depreciated],
> > 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.
>
> 4 questions:
>
> 1) Did I get the quantification wrong here? The axiom was
> supposed to say
> that if the ?FORMULA is true of the instance ?X, then that
> instance is a
> member of the ?CLASS. Wouldn't that axiom (expressed correctly) would
> always be true if we agree that is what 'criteria' means.
But I thought the "criteria" predicate was supposed to relate a class to the
formula specifying the intension of the class. Since in some cases a class
will have an intension but no extension (e.g. the class of unicorns),
defining intension in terms of extension, as the proposed axiom seems to,
seems wrongheaded. Also, the "criterion" of a class will not be a formula,
it will be a term. This term may be constructed out of a formula (as with
'KappaFn') or it may not be. In any case, I think you need to demonstrate
that there is some representational need that you have that isn't filled by
something that is already in the SUMO. In previous messages, I've tried to
show you that everything you want to formalize can be covered by the
existing conceptual apparatus.
>
> 2) It seems to me that there can be many criteria for a class
> .... perhaps
> some true in one context and false in another. Does the
> KappaFn provide for
> that reality?
I'm not sure what "reality" you're referring to here. It's true that the
same intension may have an extension in one context or possible world and
another extension in another context or possible world. This fact is
provided for in the SUMO, if we distinguish the intension of a class from
its extension.
>
> 3) Does whether instances actually exist in some context have
> any bearing on
> the truth of whether a formula is the criteria of that
> existence in that
> context ?
I'm not sure what you're asking here.
>
> 4) When are we gonna get the ability to scope formula to contexts ?
Well, that would require incorporating some version of context logic into
the SUMO. If you'd like to work on developing a SUMO-compliant version of
such a logic, we can propose adding it to the ontology.
>
> Seth Russell
>
>