SASW@MIT-MC.ARPA (Steven A. Swernofsky) (11/04/85)
Received: from CSNET-RELAY.ARPA (csnet-pdn-gw) by rand-unix.ARPA; Sun, 3 Nov 85 18:10:10 pst Received: from smu by csnet-relay.csnet id ad21012; 3 Nov 85 21:12 EST Received: by csevax.smu (4.12/4.7) id AA00249; Sun, 3 Nov 85 11:20:37 cst Date: 3 Nov 1985 11:20-CST From: leff%smu.csnet@CSNET-RELAY.ARPA Subject: Forwarded from AIList to net.math.symbolic Message-Id: <499886400/leff@smu> Date: Thu, 31 Oct 85 02:24:17 EST From: "Steven A. Swernofsky" <SASW@MIT-MC.ARPA> Subject: Seminar - Mechanical Verification of Mathematics (BBN) Thursday 31, October 10: 30am Room: BBN Labs, 10 Moulton Street, 2nd floor large conference room BBN Laboratories Science Development Program AI Seminars Toward the Mechanical Verification of Abstract Mathematics David McAllester MIT AI Laboratory To mechanically verify a mathematical argument one must translate the argument into some formal language. Many mathematicians doubt that it will ever be practical to translate arbitrary mathematical arguments into a completely formal language. This talk will present a formal language called ONTIC which extends set theory in a way that supports an "object oriented" style of mathematical description. Ontic has been used to formally define some basic concepts of modern algebra, real analysis, and homotopy theory. We feel that any branch of modern mathematics can be concisely expressed in ONTIC. Furthermore it seems practical to translate any mathematical proof into a sequence of ONTIC formulas. A theorem- proving system has been constructed for ONTIC and some simple verifications have been done.