Re: Higher-Order KIF and Conceptual Graphs
phayes@cs.uiuc.edu
Message-id: <199311111756.AA05695@dante.cs.uiuc.edu>
Reply-To: cg@cs.umn.edu
Date: Thu, 11 Nov 1993 11:58:45 +0000
To: uribe@cs.stanford.edu, fritz@rodin.wustl.edu (Fritz Lehmann)
From: phayes@cs.uiuc.edu
X-Sender: phayes@dante.cs.uiuc.edu
Subject: Re: Higher-Order KIF and Conceptual Graphs
Cc: boley@dfki.uni-kl.de, cg@cs.umn.edu, interlingua@isi.edu
At 8:19 AM 11/11/93 -0600, Fritz Lehmann wrote:
>Dear Thomas Uribe,
....... A First-Order model-
>theoretic semantics for a weakly higher-order language is no higher-
>order semantics at all -- it is still just First-Order. My original
>email inquiry in September suggested strongly higher-order
>semantics, sacrificing formal completeness and compactness but
>gaining useful expressiveness.
Oh then we *arent* arguing past one another, Fritz. Suppose we were to
agree on the utility of a higher-order syntax of some kind, for pragmatic
reasons of expressiveness in Krep. However, I will insist that we have no
warranty to claim that these quantifiers can be taken as ranging over *all*
(uncountably many) higher-order functions. You say they can: but since you
abandon completeness, you are in exactly the position of my student who
simply claims that "is-very-big" denotes what he intends it to denote.
Suppose we set up stalls opposite one another at a Krep trade fair, you
selling strong higher-order logic and me selling weak higher-order (which
we all know is really first-order) logic. Apart from the semantic theories
we put in the manuals, we will be selling the same logics. So I dont see
how you can justify your claims to this useful expressiveness that my weak
logic doesnt have. People could buy mine and tell your story about it,
after all.
Pat
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