An application of automated equational reasoning to many-valued logic
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.
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