Automating Algebraic Proofs in Algebraic Logic

Authors:
Jieh Hsiang;Anita Wasilewska
Affiliations:
(Supported in part by grant NSC 95-2221-E-002-009 of the National Science Council of the Republic of China) Department of Computer Science, National Taiwan University, Taipei, Taiwan. hsiang@csie. ...;(Supported by Fulbright grant USIA 93-68818 (1993-1994)) Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY, USA. anita@sbcs.sunysb.edu
Venue:
Fundamenta Informaticae
Year:
1996

Citing 6
Cited 0

Completion of a set of rules modulo a set of equations

SIAM Journal on Computing
On word problems in equational theories

14th International Colloquium on Automata, languages and programming
Termination of rewriting

Journal of Symbolic Computation
Complete Sets of Reductions for Some Equational Theories

Journal of the ACM (JACM)
SbReve2: A Term Rewriting Laboratory with (AC-) Unfailing Completion

RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Complete inference rules for the cancellation laws

IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 2

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present here an effective proof theory that allows one to reason within algebras of algebraic logic in a purely syntactic, algebraic fashion. We demonstrate the effectiveness of the method by discussing our automated proofs of problems and theorems taken from Professor Helena Rasiowa's book An Algebraic Approach to Non-Classical Logics, Studies in Logic and Fundation of Mathematics, Volume 78, North Holland Publishing Company, Amsterdam, London - PWN, Warsaw (1974). We include a detailed proof of a problem presented to us by Professor Helena Rasiowa in June 1993. Most of these proofs are the first direct proofs ever discovered, and they are produced by the computer without human assistance.