On intuitionistic many-valued logics

Many-Valued, Free, and Intuitionistic Logics

Standard logic is a package with two parts – a formal deductive apparatus and a conception of interpretation for the language. The deductive apparatus and the semantics are mutually reinforcing and in this chapter we examine primarily the semantic assumptions that formally justify the deductive machinery. The second part of the package, the semantics of ‘standard’ logic, includes the assumption...

Many-Valued Logics

The paper considers the fundamental notions of manyvalued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite v...

Many-valued modal logics

Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and compl...

Many - Valued Logics

Modal Systems Based on Many-valued Logics

We propose a general semantic notion of modal many-valued logic. Then, we explore the difficulties to characterize this notation in a syntactic way and analyze the existing literature with respect to this framework.