Dear Pat, (01)
Interestingly, your set of primitives does not necessarily need to form an
ontology itself at all, only be a set of terms with unambiguous reference
that can be used in axioms to define an ontology. (02)
I still think it is unlikely that there is a finite set of such terms, but
without the set of terms being proposed as an ontology itself, you have a
much better chance of success, and for me the outcome is more interesting. (03)
Another issue is where there are alternative choices of primitive. I think
that strictly it does not matter in these cases what choice you make, though
doubtless there would be great argument about the choice just for that
reason - a good case of where voting makes sense. (04)
Regards (05)
Matthew West
Information Junction
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> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Patrick Cassidy
> Sent: 04 February 2010 04:22
> To: '[ontolog-forum] '
> Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping
>
> Some comments on postings by Doug Foxvog and John Sowa:
> [DF] > These axioms apply to different types of set. If the FO is to
> include the different set theories, then it would distinguish different
> subclasses of fo:Set, e.g., fo:KPSet, fo:ZFSet, fo:KPUSet, fo:NFSet,
> etc.
> The different axioms would apply to the appropriate subclasses of set.
> Then
> mappings would be established between sets as defined in external
> ontologies
> (e.g., sumo:Set) and the appropriate subclass of fo:Set.
>
> That is my intuition, but I do not know how to prove that *every* pair
> of
> incompatible theories can be specified by axioms using some common set
> of
> agreed terms. To make the FO project worth funding, don't think it is
> necessary to prove that *mathematically*, but if we can conclude that
> exceptions would be rare, I think that would provide a case for a
> serious
> effort to try the "primitives" route to semantic interoperability. And
> if
> not, an FO might still be stable enough for practical use - it would
> just
> have to be tested to see how it works in practice.
>
> [JS] > >
> > As soon as you add more axioms to a theory, the "meaning" of the
> > so-called "primitives" changes.
> >
> I am not certain that that is true. If one adds subtypes to the types
> of
> an ontology, and each subtype has some properties or restrictions not
> applying to the parent, then it does not seem to me that the *meaning*
> of
> any of the parents changes, though we are asserting more information
> about
> the properties of the parents (i.e. that some instances have or may
> have
> certain properties). I would not consider that a change in meaning.
> If we
> discover a new animal that does not have any special properties other
> than
> being a species different from other known animals, does that change
> the
> "meaning" of the term animal? Would an inference engine be able to
> conclude
> more inferences about the parent - or some instance of the parent not
> specified as being one of the new subtypes?
>
>
> [JS] > > You could call subsetOf and elementOf primitives, but they
> don't
> > behave the way that you have been claiming for the kinds of
> > primitives you want. In particular, their "meaning" is determined
> > by the axioms and each version of set theory has a different set
> > of axioms.
> >
> If the logical inferences for those relations holding differ in
> different
> theories, it would seem to me that those are different relations. I
> would
> need specific examples to be able to see what you mean by a "different
> meaning", to see how to handle such cases.
>
> Pat
>
> Patrick Cassidy
> MICRA, Inc.
> 908-561-3416
> cell: 908-565-4053
> cassidy@xxxxxxxxx
>
>
> > -----Original Message-----
> > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> > bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> > Sent: Wednesday, February 03, 2010 10:48 PM
> > To: [ontolog-forum]
> > Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping
> >
> > Pat and Chris M,
> >
> > PC> Thanks, that is getting closer to specifics, but I am still
> unclear
> > > exactly where the logical inconsistencies lie.
> >
> > The inconsistencies lie in the choice of axioms. All versions of set
> > theory are based on two dyadic relations: subsetOf and elementOf.
> > The differences lie in the axioms that are asserted in each theory.
> >
> > You could call subsetOf and elementOf primitives, but they don't
> > behave the way that you have been claiming for the kinds of
> > primitives you want. In particular, their "meaning" is determined
> > by the axioms and each version of set theory has a different set
> > of axioms.
> >
> > That is one of the main reasons why I keep saying that this search
> > for primitives is misguided. It's totally irrelevant what set of
> > words (or predicates or relations or types or concepts or whatever)
> > you start with -- because all the serious work is done by the axioms.
> >
> > As soon as you add more axioms to a theory, the "meaning" of the
> > so-called "primitives" changes.
> >
> > John
> >
> >
> >
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