Examples- Higher-Order KIF and Conceptual graphs

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Reply-To: cg@cs.umn.edu
Date: Thu, 11 Nov 93 16:40:56 -0500
From: Dan Schwartz <schwartz@iota.cs.fsu.edu>
Message-id: <9311112140.AA01365@iota.cs.fsu.edu>
To: cg@cs.umn.edu, interlingua@ISI.EDU
Subject: Examples- Higher-Order KIF and Conceptual graphs

Fritz Lehman writes:

>[33]. [DAN SCHWARTZ'S EXAMPLE]  Combination of classical outer
>logic with fuzzy inner logic.  [This initially strikes me as a
>meta-level issue rather than a logic-order issue.]
>
>[34]. [DAN SCHWARTZ'S EXAMPLE]  Combination of quantification,
>likelihood, and usuality.  [Same comment.]

Yes, that's right; it's the meta-level.  I have to admit some confusion
over terminology as it has been appearing on this email list lately.  To
me, FOL means First Order Logic as in Mendelson or Shoenfield, and HOL
means essentially Second Order Logic as was used to formulate various
versions of set theory.  (I have understood/believed that there was
really no need to go to higher than second-order, as such could always
be reduced to second-order).  Recently, though, I've noted John Sowa
using "FOL" to refer to higher-leveled systems in which some variables
range over syntactical elements (e.g.  proposition variables).  My
interpretation of this has been that a second-level FOL embodies a
formalization of part of the metalanguage of a first-level FOL.  I guess
I was mixed up regarding whether you meant ``higher-order'' in the usual
sense, or ``higher-level'' in the latter sense.

At issue for me, though, is whether such systems as the above two can be
expressed in the KIF/CG formalisms.  I am encouraged that they can, by
John's remarks that CG's accomodates higher-leveled FOL's.  However, if
they can't, then this reveals a limitation in those formalisms as
providing a basis for general knowledge representation.

--Dan

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Daniel G. Schwartz                                Office    904-644-5875
Dept. of Computer Science, MC 4019                CS Dept   904-644-2296
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