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From: jbn@wdl1.UUCP (jbn )
Newsgroups: net.ai
Subject: Re: Now and Then
Message-ID: <424@wdl1.UUCP>
Date: Mon, 17-Sep-84 21:21:16 EDT
Article-I.D.: wdl1.424
Posted: Mon Sep 17 21:21:16 1984
Date-Received: Tue, 25-Sep-84 03:20:09 EDT
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Nf-From: wdl1!jbn    Sep 17 17:16:00 1984


     Having spent some years working on automatic theorem proving and
program verification, I am occasionally distressed to see the ways in which
the AI community uses (and abuses) formal logic.  Always bear in mind that
for a deductive system to generate only true statements, the axioms of the
system must not imply a contradiction; in other words, it must be impossible
to deduce TRUE = FALSE.  In a system with a contradiction, any statement,
however meaningless, can be generated by deductive means.
     It is difficult to ensure the soundness of one's axioms.  See Boyer
and Moore's ``A Computational Logic'' for a description of a logic for which
soundness can be demonstrated and a program which generates inductive proofs
based on that logic.  The Boyer and Moore approach works only for mathematical
objects constructed in a specific and rigorous manner.  It is not applicable
to ``real world reasoning.''
     There are schemes such as nonmonotonic reasoning which attempt to deal
with contradictions.  These are not logical systems but heuristic systems.
Some risk of incorrect results is accepted in exchange for the ability to
``reason'' with non-rigorous data.  A clear distinction should be made between
mathematical deduction in rigorous spaces and heuristic problem solving by
semi-logical means.  

				John Nagle