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From: aarons@syma.sussex.ac.uk (Aaron Sloman)
Newsgroups: comp.ai
Subject: Re: Unified model for knowledge representation? (Impossible)
Summary: it ain't possible
Message-ID: <5255@syma.sussex.ac.uk>
Date: 2 Jun 91 13:55:35 GMT
References: <1991May31.164608.238@nmt.edu>
Organization: School of Cognitive & Computing Sciences, Sussex Univ. UK
Lines: 65

francia@nmt.edu (Guillermo A. Francia) writes:

> Date: 31 May 91 16:46:08 GMT
> Organization: New Mexico Tech
>
>
> In as much as there are a number of means to represent (or code)
> knowledge in AI, I would like to know if anyone has done any
> research on a UNIFIED (mathematical) model of knowledge representation.
> Does anyone out there know of any work done on this?
>
> --------------------------------------------------------------------
> francia@jupiter.nmt.edu                     Guillermo A. Francia III
> 					    P.O. Box 2335 CS
> francia@minos.nmt.edu			    New Mexico Tech	

Some of the people who have worked on first order logic have thought
it could serve as the universal (= unified?) notation for
representing knowledge. I don't know if this is what you mean by a
model.

However, it seems pretty obvious from the history of science and
culture that different formalisms are useful for different purposes,
including, logic, algebra, pictures, maps, tables, flow-charts,
musical notation, 3-D models, natural languages, etc.

One reason for this is that different kinds of notations have
different kinds of variability, which limits their expressive power
in different ways. This can sometimes be important when exploring
large search spaces. If the structure of the notation is such that
it won't let you express things that would only be rejected anyway,
it can have great heuristic power.

Equally if the structure of the notation is such that certain
frequently used forms of inference can be done with simple
algorithms, that is also useful. (E.g. roman numerals are very good
for addition: simply concatentate the numerals, provided that the
numbers you are adding total no more than III ! Arabic numerals are
an ad-hoc but very useful notation, good for a wider range of
operations, but not all that powerful when it comes to taking square
roots, dividing large numbers that are not powers of 10, etc.)

AI has so far explored only a tiny subset of possible forms of
knowledge representation, mostly the ones that are easiest to
manipulate using current computers and programming languages.

I don't think that anyone will ever find a
    "UNIFIED (mathematical) model of knowledge representation"
unless it takes the form of a sort of meta-theory explaining why
different models are needed for different knowledge domains
and different kinds of uses of knowledge.

If anyone claims to have a unified model, ask him/her if it will
serve for the purposes of representing knowledge about the contents
of the current optic array in a robot's visual system, and for
transforming that knowledge in the process of discovering what's out
there (e.g. discovering binocular disparities for stereo vision) or
for fine control of posture and actions, etc.

Aaron Sloman,
School of Cognitive and Computing Sciences,
Univ of Sussex, Brighton, BN1 9QH, England
    EMAIL   aarons@cogs.sussex.ac.uk
or:
            aarons%uk.ac.sussex.cogs@nsfnet-relay.ac.uk