Re: SUO: intention vs. extension again
> > >Note that this issue arises for most common properties of, and relations
> > >among, classes; e.g., transitivity, reflexivity, subclass, etc.
> >
> > I agree. Does having implication for the similar axioms that define these
> > relations seem right to you?
>
>I'm in two minds about disjointness, since both its weaker and stronger
>forms are useful. However, it does seem to me that when anyone other
>than Pat Hayes sez that a relation is symmetric, say, they are saying
>something more than that it just happens to be the case that Rxy implies
>Ryx for all the x and y that we happen to be talking about at the
>moment.
That isnt what I mean either. What I mean is that for ALL x and y,
Rxy implies Ryx, which is what the logical axiom says. That is a
universal quantifier in there, and it makes no reference to 'what we
are talking about at the moment'. (I wonder, in fact, where in the
model theory you manage to find that notion of 'all that we happen to
be talking about at the moment'. Is that a new KIF quantifier?) The
univeral quantified form is exactly what is meant by virtually all
mathematicians, everyone in the DAML world, all description/class
logics (such as OIL, CLASSIC, LOOM and so on), throughout database
theory, and by everyone I know who is doing Krep. It is the sense
used in Cyc. The only ones who disagree would be those whose primary
interest is in NL applications, and a few loony philosophical
logicians.
>I don't think loving would be a symmetrical relation even if
>for one brief shining moment, or even through all of history, all love
>happened to be requited.
Chris, please don't misrepresent me. I agree with you about the love
example. The point is, however, that the axioms in ontologies are not
(usually) though of as a set of truths AT A MOMENT, but are rather a
theory OF AN ENTIRE WORLD. When I quantify over ALL things, I really
intend it to mean 'all'. It ranges over the UNIVERSE, not some subset
of things-we-happen-to-be-talking-about. Ontological content is not
tensed, it is not English conversation or transient beliefs which are
changing from moment to moment, particularly at the 'upper' levels,
which presumably, no matter exactly where we draw the boundaries of
'upper', are supposed to be at least above ground atomic facts in the
present tense.
My diatribes against the use of modal reasoning to represent rigidity
are based on this point. The modalities refer (implicitly, but that's
another issue) to possible worlds other than a 'present' world.
Rigidity refers to changes to the knowledge base. There is absolutely
no connection (other than some external imposition by fiat) between
the 'worlds' referred to by the modalities and the 'worlds'
consisting of the states of the Kbase. They have nothing whatever to
do with one another. If they did - if there was any way to ensure
that the modally possible worlds were, or corresponded to, the
'worlds' gotten by changing the Kbase, then of course this would all
work (though I would still prefer to avoid modalities for other
reasons, but leave that aside for now.). And if you are thinking of a
temporally located agent, reasoning about its own temporal progress
through the world which is changing as time flows by, (like us
humans, for example, and the languages we use to reason about our own
pasts and futures) then indeed there is such a guarantee. But that
picture has NO place in logical semantics, in spite of its appeal
when thinking about natural language.
Until someone comes up with a model theory which explicitly considers
states of the Kbase and changes in it, any claim of a connection
between modality and rigidity is just handwaving. God knows we have
enough handwaving on this discussion group already.
Pat
---------------------------------------------------------------------
IHMC (850)434 8903 home
40 South Alcaniz St. (850)202 4416 office
Pensacola, FL 32501 (850)202 4440 fax
phayes@ai.uwf.edu
http://www.coginst.uwf.edu/~phayes