Dual Tableaux for Many-Valued Logics

Abstract

The development of multiple-valued logic in its modern form began with the work of Jan Łukasiewicz [Łuk20] and Emil Post [Pos20, Pos21]. Since the emergence of computer science as an independent discipline, there have been an extensive interplay and mutual inspiration between the two fields. Apart from its logical and philosophical motivation, multiple-valued logic has applications, among others, in hardware design and artificial intelligence. In the field of hardware design classical propositional logic is used as a tool for specification and analysis of electrical switching circuits with two stable voltage levels. A generalization to a finitely-valued logic allows the analogous applications with possibly many stable states. In artificial intelligence multiple-valued logic provides models of vagueness or uncertainty of information and contributes to the development of formal methods simulating commonsense reasoning. Some recent developments and applications of multiple-valued logics can be found e.g., in [Mal93, Got00, Häh01, FO03].