Tutorial: Complexity of many-valued logics

Abstract

Like in the case of classical logic and other non-standard logics, a variety of complexity-related questions can be asked in the context of many-valued logic. Some questions, such as the complexity of the sets of satisfiable and valid formulas in various logics, are completely standard; others, such as the maximal size of representations of many-valued connectives, only make sense in a many-valued context. In this overview I concentrate mainly on two kinds of complexity problems related to many-valued logics: I discuss the complexity of the membership problem in various languages, such as the satisfiable, respectively, the valid formulas in some well-known logics. Two basic proof techniques an presented in some detail: a reduction of many-valued logic to mixed integer programming and a reduction to classical logic.