Re: Higher-order KIF & Conceptual Graphs (Chris Menzel)
From: (Chris Menzel)
Message-id: <>
Subject: Re: Higher-order KIF & Conceptual Graphs
To: (Fritz Lehmann)
Date: Fri, 21 Jan 1994 09:46:49 -0600 (CST)
Cc:, interlingua@ISI.EDU,
In-reply-to: <> from "Fritz Lehmann" at Jan 21, 94 05:04:33 am
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Fritz Lehmann wrote:
>      The "logical foundations" KIF committee which Pat Hayes is
> to head should have some balance, if it is to properly address
> the issue of whether to use real, classical higher-order semantics,
> or just a schema-based First-Order imitation for the sake of
> completeness and compactness.  

The point about balance is well taken, but the way the issue is
phrased suggests that preservation of completeness and compactness is
the only reason for opting for first-order semantics.

>      I surmise that Conceptual Graphs' formal semantics will
> mainly be in John Sowa's hands (except to the extent that he might
> elect to defer to the KIF committee).  He was spirited in his
> defense of a particular brand of First-Orderism which excludes
> numbers from the model-theoretic semantics and takes them as a
> kind of semantic primitive.  

I don't think it would be correct to say that John suggested excluding
numbers from the model theoretic semantics, though I might be
misunderstanding; I'm not sure exactly what it would be to do so.  My
understanding of John's view, from the perspective of model theory, is
that he puts a constraint on acceptable models of an interlingua: such
models must interpret the predicates "NUMBER", "SUCCESSOR", etc. in
such a fashion that the NUMBERs of the model are isomorphic to the
numbers, i.e., the NUMBERs of the model must form an omega-sequence
under the SUCCESSOR relation.  That way, one is guaranteed that, e.g.,
when one defines a set in the model to be FINITE just in case it is
enumerated by some NUMBER (however one decides to cash this out) it
*really is* finite in the model.  This is exactly analogous to the
sort of stipulation that the friends of higher-order semantics make
vis-a-vis the interpretation of higher-order quantifiers, and suggests
that John's particular brand of first-orderism is pretty flexible.

> P.P.S. Must we totally neglect intension?  Sinn?  Two facts
> are: A. There are too many different discordant notions of
> what "intensions" are and many are hard to formalize neatly,...

But there are several very neat formalizations, in particular, those
of Montague, Cresswell and other possible worlds theorists for
"coarse-grained" accounts of intensions (i.e., accounts on which
intensions are identical if necessarily equivalent), and, for
"fine-grained" intensions Bealer (in, e.g., Quality and Concept,
Oxford, ~1980) and Zalta (in Abstract Objects, Reidel, ~1980).

> B. Notwithstanding fact A., intensions really matter more than
> extensions.  Triangularity is the thing to know about, not the set
> of triangles.  Same goes for Democracy, puffinhood and FAX machines.
> Who really cares about arbitrary extensional sets of objects?
> Extensional logic is neat and easy, but it's just a constraint on
> the logic that matters.  Pegasus is not a golden mountain, for one
> thing, even if their empty extensions are the same.  This is a big
> issue for Knowledge Representation, or should be.


Christopher Menzel		    Internet ->
Philosophy, Texas A&M University    Phone ---->   (409) 845-8764
College Station, TX  77843-4237	    Fax ------>   (409) 845-0458