Re: Higher-Order KIF and Conceptual Graphs
Message-id: <>
Date: Thu, 11 Nov 1993 11:58:45 +0000
To:, (Fritz Lehmann)
Subject: Re: Higher-Order KIF and Conceptual Graphs
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.


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