RE: SUO: Vote on Merged Ontology as a 'Base Document' for SUO WG
If I understand you correctly, you spell out two broad criticisms of
the "Merged Ontology" in this message.
1. Quantifiers in one ontology may range over a very different universe of
discourse from the axioms in another ontology.
2. In some cases it is not possible to create a simple, one-to-one mapping
between the relations/predicates in one ontology and the
relations/predicates in another ontology.
I agree with both of these points, but I don't see that they move the
discussion forward. If you don't indicate to me exactly where in the latest
version of the "Merged Ontology" I have misconstrued the range of a
quantifier or incorrectly mapped a relation/predicate, I can't improve the
quality of my document and other members of the group cannot decide for
themselves whether the "Merged Ontology" should be accepted as a "base
document". I know that you did provide this sort of detailed criticism with
respect to the first version of the "Merged Ontology", and this criticism
was much appreciated and was incorporated into the second version. However,
I don't see that disparaging remarks in the absence of substantiating
examples are very useful if our aim is to converge on a single, upper level
> -----Original Message-----
> From: pat hayes [mailto:email@example.com]
> Sent: Tuesday, January 16, 2001 3:37 PM
> To: Adam Pease
> Cc: firstname.lastname@example.org
> Subject: Re: SUO: Vote on Merged Ontology as a 'Base Document' for SUO
> > Our work can only proceed by people making concrete suggestions
> >about how to reconcile, integrate and improve the content we're
> >starting with.
> Adam, greetings. You are making a central mistake here. Axioms do not
> comprise content. We don't have ANY content until we know what an
> axiomatic ontology claims to be about. First we have to determine
> what the content of an ontology actually IS. Once we have that
> reasonably clear, we can make a start on trying to integrate two of
> Look at the ontologies which Niles has cobbled together here, and ask
> what they are supposed to be about. There is the Casarti/Varzi
> ontology of 'holes', whose axioms contain quantifiers which are
> intended to range over a certain subclass of pieces of space (those
> which can be thought of as holes in some other, physical, object).
> Then there is the overarching Entire Theory of the Universe
> represented by John Sowa's upper-level ontology classification.
> Evidently, when one of John's axioms uses a 'forall', it doesnt mean
> the same as what one of C&V's axioms mean when it uses a 'forall';
> John's universal quantifier ranges over a much, much larger set of
> things than the C&V universal quantifers do. Its not even clear to me
> that the range of the C&V quantifiers can be characterised within the
> classification scheme which Niles has extracted from John, in fact .
> (I'm sure that there are several Sowa-classs into which the
> C&V-quantifications can be placed, but I am not at all sure there is
> one that fits them exactly, which is what we need in order to put a
> suitable restriction onto the quantifiers in the C&V axioms.) Every
> 'source' from which Niles has lifted axioms has a distinct notion of
> what is in its universe, and the axioms were written with that
> universe in mind. That is what I meant by saying that the various
> parts of Niles' axiom-collection have incompatible assumptions. When
> you move a universal quantifer from one universe to another, the
> likelihood of its remaining true is vanishingly small.
> > It's easy to say that any proposal is inadequate. My hope is that
> >you and others with propose specific improvements. Ian has done
> >considerably more than just merge sources into a common notation.
> > Certainly, different ontologies may not have strong connections
> >with one another. I don't believe that is required. Every branch
> >of a tree need not be strongly connected to a large set of siblings.
> >The important features I would say are that the branches are not
> >inconsistent or redundant. I believe that has been achieved.
> I am absolutely certain that it has not. I am not talking about
> branches of a tree; that is beside the point (and also, incidentally,
> misunderstands the nature of Sowa'a classification scheme, which is
> lattice-based rather than tree-like.) My point (which Ive already
> made to Niles) is that every time one adjoins an axiom from one
> ontology into another ontology, you have to carefully re-think
> exactly what every quantifier means, and ask youself whether, and if
> so how, the intended meaning of the quantification can be stated in
> the larger, merged, ontology. You also need to ask youself what all
> the relation names mean and now they need to be translated into the
> other terminology. Sometimes they might, if you are remarkably lucky,
> translate into relations there as well. More likely they will have to
> be rendered as quantified restrictions on other relations, so that (R
> A B) might have to be translated as something like
> (exists (?y)(and(implies (phi ?y) (R1 A ?y)) (implies (rho ?y)(R2 B
> ?y)) )), where rho and phi are themselves complex assertions. This
> means that a simple universal quantification becomes an nested
> quantifier statement which will generate new nonlogical vocabulary
> when skolemised, and there is good chance that you will need new
> axioms for those skolem functions when you start thinking about what
> they mean. We found that even in translating between alternative
> axiom systems for mereotopology that there were cases where a simple
> relational assertion became a triply nested quantification scheme,
> and a two-line axiom translated into expressions with five nested
> alternating quantifiers, just because one world view only quantified
> over regular sets, and the other allowed surface and edge fragments
> to be first-class entities. God alone knows what would have happened
> if there had been things like nexuses and abstracta and firstnesses
> in the universe as well.
> >The tree may be considered sparse or denuded, but that's to be
> >expected at this early stage.
> A bundle of sticks is not a tree.
> Pat Hayes
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