Re: SEMIS Bulletin
(slightly revised from an earlier version sent to
some of the above addressees)
Some comments about FOL, in relation to information
flow.
John F. Sowa wrote:
> Unfortunately, the STEP group, on average, is no better grounded
> in logic than the W3C. The fact that EXPRESS happens to have
> the expressive power of FOL is due to luck: If you want to
> translate natural language spec's into any declarative notation,
> it will inevitably include the full power of FOL.
I don't think there is anything wrong with FOL in particular,
and certainly not in Frege and Russell's original domain of
mathematics, where objects are universals and unchanging forms.
But when using it with natural language and the
non-mathematical domains it describes, FOL is too
powerful, and doesn't pay enough attention to tokens.
Ignoring tokens is fine for mathematics, where classifications
are always extensional and separated. You just have
extensional sets of types, and infomorphisms turn into
Galois connections. In particular, you can turn
relations and functions into derived notions, with the
usual set-theoretic definitions. Some have suggested
that a property-theoretic approach is more suitable
outside of mathematics, and that properties and
relations are primitive, and not reducible to (sub)sets
of (cross products of sets of) elements or atoms.
Barwise and Perry's Situation Theory is an example
of a property-theoretic approach to modeling beyond
mathematics, and Barwise and Seligman's _Information Flow_
was designed to accommodate that (as well as set theory).
So I think the problem in bringing back logic from
mathematics to the world is to constrain the power of
FOL without losing its benefits. Nonmonotonic
logics are even more powerful, and so are HOL's.
What we can give up is the closed world assumptions
of mathematics, and fix a classification where classical
logic will hold (or we could use an HOL base, if we
need to incorporate reification somewhere), but also
look at structures for moving between classifications
where some of the assumptions of classical (mathematical)
logic fail. A particular ontology application may or
may not want to do this, but surely it is worthwhile
when trying to map between ontologies.
In fact, computers aren't mathematics either, and building
on Domain Theory, people like Vaughn Pratt have gotten
excited about Chu spaces (the same category as IF
classifications) for modeling concurrency, and other things.
B&S's IF is applicable for representation systems
(mathematics, computers and natural language) as
well as other things those representations might be
about. Kent's IFF suggests that this is useful for
ontology integration, but I still can figure out how
that can be done. Kalfoglou and Schorlemmer give some
examples of IF based ontology mapping,
http://www.ecs.soton.ac.uk/~yk1/publications.html .
I am still left wondering if it can scale to integrating
with larger systems like Cyc, what kinds of tools and
standards will be needed, and how various ontology
initiatives can instrument themselves for easy integration.
Looking at some of the philosophical underpinnings,
perhaps the virtue of Peirce is his Aristotelian interest
in logic used more broadly than mathematics. Russell
and Frege seem more in a Platonist and Hegelian
(and as the later Wittgenstein points out Augustinian)
tradition, and when their work was taken over by
the logical empiricists, we got a rather reductionist
naturalism for things like facts in general and representations
in particular. I can't say I know what Peirce's Thirdness
is about, but is seems a plausible base for improving
on the narrow perspective of Russell and others. Now
how does one link the mathematics of information flow
to Peirce? I bought Peirce's _Reasoning and the Logic
of Things_, I don't know if that is a good starting point.
In a different thread, perhaps somebody might want
to take a stab at relating Peirce and information flow?
So I don't think the problem is full FOL versus a more
restricted DL. I think that for many reasons including
computational tractability, we should fix classifications
and use FOL-like inference, then have techniques for
mapping between classifications, where certain FOL
characteristics, including in a restricted way monotonicity,
will fail. That doesn't mean our tools our defective,
in the real world information flow is often imperfect.
The closed world perfect truths of FOL are illusory
when you step outside mathematics or Augustinian theology.
We should be looking for conditions of successful information
flow (or Searle's conditions of satisfaction for speech
acts) rather than truth-conditional semantics.
Cheers,
Fred
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Frederick B. Kintanar
Cebu City