Chapter 20 - Automated Deduction for Many-Valued Logics

Abstract

This chapter deals with the demarcation of the realm of logics. It is a less simple task as it may seem at first glance. Traditionally, any logic characterized by a semantic based on more than two truth values is called “many-valued” or “multiple-valued.” However, only ideological or historical reasons would drive us to exclude classical two-valued logic from the realm of all many-valued logics. Indeed, although historically particular many-valued logics have been presented as alternatives to classical logic, from the viewpoint of computer science, it is often much more appropriate to study broad families of many-valued logics as generalizations of classical logic. It is well known that some logics that have originally been represented in quite different semantic contexts (like the modal logic S5) have later been recognized to have “natural” many-valued semantics or to coincide extensionally with well-known many-valued logics. This is particularly true if one considers infinitely many truth values. In fact, in a very abstract sense, every logic can be viewed as a many-valued one. More restricted definitions of “many-valuedness” have been suggested but always depend on the intended context of investigation.