Abstract
In this paper we present a new set of axioms of an algebaric nature, for the many-valued logic of Lukasiewicz. These axioms are similar to those given by J.Hsiang for the Boolean Algebra. The equivalence of our set of axioms with those given by Lukasiewicz himself is proved mechanically, by resorting to the Automatic UKB-based Equational Theorem Prover SBR3. These new axioms may be helpful for further equational reasoning in such logics, or for interpreting the ‘equality symbol’ of linear logic. This paper is organized as follows. Section 1 presents briefly the many-valued logic. Section 2 indicates the proof-steps leading to our new set of axioms. Section 3 presents the equational prover SBR3.
Research supported in part by NSF grants INT-8715231, CCR-8805734 and CCR-8901322. Also supported by Dottorato di Ricerca in Informatica, Universitá degli Studi di Milano.
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References
S.Anantharaman, N. Andrianarivelo, Heuristic Criteria in Refutational Theorem Proving, Research-Report, LRI-Orsay(Fr.), no. 541, 1990, Extended-Abstract in Proc. DISCO'90, LNCS. no. 429
S.Anantharaman, N. Andrianarivelo, A Complete Semi-Decision Procedure for Horn Theories, Research Report, LIFO-LRI(Fr.), (to appear in Feb.-March 1991)
S.Anantharaman, J.Hsiang, Automated Proofs of the Moufang Identities in Alternative Rings, Vol. 1, J. Automated Reasoning, 1990
S. Anantharaman, J. Hsiang, J. Mzali, SbReve2: A term rewriting laboratory with (AC-)Unfailing Completion, RTA, Springer-Verlag LNCS Vol. 355, pp533–537, 1989
S.Anantharaman, J.Mzali, Unfailing Completion Modulo a set of Equations, Research Report, no. 470, LRI-Orsay (Fr.), 1989
L.Bachmair, N.Dershowitz, D.Plaisted, Completion without failure, Proc. Coll. on Resolution of Equations in Algebraic Structures, Lakeway, Texas, 1987
N. Dershowitz, A Maximal-Literal Unit Strategy for Horn Clauses, Proc. of the 2nd CTRS, Montreal, 1990
J.M. Font, A.J. Rodriguez, A. Torrens, Wajsberg algebras, Stochastica, Vol. 8, No. 1, pp5–31, 1984
J. Hsiang, M. Rusinowitch, On word problems in equational theories, 14th ICALP, Springer-Verlag LNCS Vol. 267, pp54–71, 1987
J. Hsiang, M. Rusinowitch, K. Sakai, Complete set of inference rules for the cancellation laws, IJCAI 87, Milan, Italy, 1987
P. Lescanne, Computer Experiments with the REVE term rewriting system generator, 10th POPL, pp99–108, 1983
D.Mundici, Personal communication.
A. Tarski, J. Lukasiewicz, Investigations into the sentential calculus, Chapter 4th in A.Tarski, Logic, Semantics, Meta-mathematics, pp38–56, Clarendon Press, Oxford, 19
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Anantharaman, S., Bonacina, M.P. (1991). An application of automated equational reasoning to many-valued logic. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_88
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DOI: https://doi.org/10.1007/3-540-54317-1_88
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