Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!decwrl!amd!fortune!wdl1!jbn 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 Lines: 22 Nf-ID: #R:sri-arpa:-1317900:wdl1:1100001:000:1334 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