Abstract

In this paper we study the logic Ł*, introduced by C. C. Chang as a natural extension of Łukasiewicz' logic Ł. This logic has positive and negative truth values in the real number interval [−1,1].We study deductive filters, we prove a deduction theorem and give detailed proofs of the soundness and completeness theorems. In the last section, we prove that the tautology problem for the logic Ł* is co-NP.This paper is to be considered a continuation of the paper MV*-Algebras, by the same authors and appearing in this same volume. In that paper we study a class of algebras introduced by Chang as what is now known as an equivalent algebraic semantics for the logic Ł. For most definitions and other algebraic concepts, the reader is referred to that paper