From: axs@cs.bham.ac.uk (Aaron Sloman)
Newsgroups: comp.ai
Subject: Re: Human intelligence vs. Machine intelligence
Summary: there are at least two kinds of consistency
Date: 11 Oct 92 21:37:34 GMT
Organization: School of Computer Science, University of Birmingham, UK

cam@castle.ed.ac.uk (Chris Malcolm) writes:

> Date: 11 Oct 92 19:36:11 GMT
> In article <burt.718665726@aupair.cs.athabascau.ca> burt@aupair.cs.athabascau.ca (Burt Voorhees) writes:
>
> |   As I have underwstood it, the strong AI position is that it is possible
> | to create intelligent behavior on sequential machines running formal
> | programs.  Last I heard formal programs were required to be based on
> | consistent formal systems.
>
> This is not the strong AI position, it is the ridiculously
> muscle-bound AI position. Since it is possible to write computer
> programs (which turn out on analysis to be) based on inconsistent
> formal systems, and if these are therefore not formal programs, what
> are they? Informal programs?

I agree with what Chris is saying, but think it needs to be
expanded. I suspect there's a confusion here between two kinds of
consistency:

(a) A program is consistent if at every stage there are never two
inconsistent instructions for the machine to obey. Certainly every
machine code program has to be consistent in this sense. A
production system could be inconsistent in this sense, in that it
could have two rules like
    If P then 99 -> x
    If P then 88 -> x

If became true, the inconsistency might be removed by an interpreter
that dealt with such things by selecting one of the rules (using a
"conflict resolution strategy"). The inconsistency would then be
apparent but not real: the rules would not have the interpretation
they appear to have, since there would be implicit additional
conditions involved in the way the interpreter handled the rules.

(b) A program is consistent if it makes use of some kind of database
of information in which there are factual (true or false) assertions
and the assertions are all capable of being true simultaneously. If
they cannot all be true the database and therefore the program is
inconsistent.

(a) could be called procedural inconsistency, (b) factual
inconsistency.

Parents can damage their children by programming them with
procedural inconsistencies!

I suspect that Burt was talking about procedural inconsistency.
A mono-processor program that is *really* inconsistent in sense (a)
would not be able to run. Machine code programs use a representation
that make (a) impossible: at any stage there's only ONE instruction
in the instruction register.

A program that is inconsistent in sense (b) could function as well
as human beings who have globally inconsistent sets of beliefs, but
who always base individual actions on some subset.

It is arguable that intelligent systems cannot avoid factual
inconsistency of type (b):
    (1) because errors will always creep in because of the
    difficulty of getting everything right first time and the
    computational complexity of detecting and removing factual
    inconsistency in large knowledge stores would be crippling (it
    can require a number of steps that is an exponential function of
    the number of independently variable items in the database)
and
    (2) because the world has a type of complexity that makes it
    unmanagable for purposes of rational decision-making unless you
    make all sorts of simplifying assumptions, and those assumptions
    will inevitabely be globally inconsistent (like "wooden tables
    are solid and impenetrable", in everyday life and "wooden tables
    are mostly empty space and continually penetrated by sub-atomic
    particles", in the physics lab.)

In the context of Godel, Lucas and Penrose, it becomes crucial then
to be clear which sort of consistency is in question. Penrose tries
to restrict his discussion to a formal system F that characterises
arithmetic (which suffices for Godel's purposes), and Penrose
produces only circumstantial evidence that it must be consistent.
(His evidence has to do with the success of mathematics and the
critical power of the mathematical community, if I remember
correctly.)

My argument, summarised very briefly in an earlier posting, is that
even if F is consistent, Penrose is deluded in thinking that he can
use Godel's theorem as a basis for discovering that the Godel
sentence G(F) is true. Many of his critics share the same delusion.

The full argument requires very detailed analysis of what the Godel
formula actually says: I claim it merely says that a very
complicated arithmetical property belongs to a certain very large
number. It gets subtly misinterpreted as saying something about a
certain formula and its relationship to a formal system.

Aaron
-- 
Aaron Sloman, School of Computer Science,
The University of Birmingham, B15 2TT, England
EMAIL   A.Sloman@cs.bham.ac.uk  OR A.Sloman@bham.ac.uk
Phone: +44-(0)21-414-3711       Fax:   +44-(0)21-414-4281
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