Re: Equality and subclass axioms

On Mon, 27 Nov 2000, pat hayes wrote:

> Jeff Heflin wrote:
> >Ian Horrocks wrote:
> > >
> > > You didn't "negate" my axiom (you can never do that), you just added some
> > > additional information (an additional constraint). Assuming it is true
> > > that no model can allow triangles that are both three and four-sided, then
> > > this is an example of the kind of "over-constraining" that I mentioned in
> > > my email: our ontology now constrains allowable models to the extent that
> > > none can ever contain an instance of triangle (i.e., we can infer that
> > > triangle is equivalent to the class "Nothing"). If we use a reasoner to
> > > check the ontology generated by our crawler, then it will detect this
> > > fact, and can alert an intelligent (possibly human) agent to the fact that
> > > there may be a problem with the axioms relating to triangle.
> > >
> >
> >But how can a system know when a particular definition is
> >"over-constrained" and when an equivalence to "Nothing" is actually
> >intended? Is a human going have to step in every time "Nothing" is
> >defined and say, "Yes, I really meant 'Nothing'?" I hope not, because I
> >can see ontology integration as a frequent occurence. I think that
> >semantic search engines will need to be able to integrate ontologies on
> >the fly to meet the needs/context of each query issued by a user. I
> >don't believe you can have a single integrated ontology that works for
> >all queries.
> There may be a problem of nomenclature here. "Over-constrained" in 
> this sense just means "inconsistent". In a sense Ian is right, that 
> (monotonic) logic only allows one to add information, so that it is 
> impossible to "negate" an assertion with another, if this means 
> something like 'erase' or 'nullify'. But this is slightly 
> disingenuous, since it IS possible to contradict one assertion with 
> another. If A asserts P and B asserts not-P, then we usually would 
> say that they disagree, or are contradicting each other. Translated 
> into Horrocks-talk, this means that the conjunction of their 
> assertions (P and not-P) is so over-constrained that there is no 
> possible way to interpret it as describing a state of affairs, ie 
> what A says about the world cannot be reconciled with - contradicts - 
> what B says about it.

I was trying to make a serious point, not to engage in disingenuous
double-talk. In the triangle example, what A and B assert is not P and
not-P, but "X <-> P and X <-> Q, where P -> not-Q. From this we can infer
that there is no such thing as an X (or a P, or a Q), just because this is
the only state of affairs in which both assertions hold. In some
circumstances (like our triangle example) the inference may be trivial,
and/or may conflict with our intuition; in this case we may want to
conclude that A and B "disagree", and that the ontology is "incorrect". In
other circumstances the inference may be non-trivial and/or consistent
with our intuition; in this case we may want to conclude that both A and B
were "correct", and that by combining their knowledge we have discovered
some new and useful fact.


Received on Tuesday, 28 November 2000 06:41:32 UTC