Re: How do I learn to represent knowledge? (Fritz Lehmann)
Date: Tue, 12 Jul 94 21:29:00 CDT
From: (Fritz Lehmann)
Message-id: <>
Subject: Re: How do I learn to represent knowledge?
References: <2v8i4p$> <2vpn6e$>
Organization: Center for Optimization and Semantic Control, Washington University
Precedence: bulk
     Jorn Barger disparages formalizing too soon, and I agree, 
but formalizations can accommodate the "complex" concepts
mentioned by Barger.  Keep in mind that not only concepts
(represented by monadic predicates) but also n-adic 
relations occur in hierarchies (subsumption posets).  Given
such hierarchies, a description (omitting negation) is
an order-sorted directed hypergraph (relational structure).
Such structures occur in an _induced_ (or "lifted")
hierarchy of their own.  The latter is a function of:
A. The separate contributing hierarchies of predicates
and relations, and B. The universal poset of directed
hypergraph inclusion (based either on subhypergraph isomorphism
or on homomorphism up to hom-equivalence).  My "skeleton
product" and "fret product" determine the shape of the
resulting hierarchy.  These have to take account of
structural symmetries, since every description is an abstract
semantic structure "up to isomorphism" and symmetric syntactic
variants are irrelevant.

                          Yours truly,   Fritz Lehmann
GRANDAI Software, 4282 Sandburg Way, Irvine, CA 92715, U.S.A.
Tel:(714)-733-0566  Fax:(714)-733-0506