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From ERCIM Working Group on Many-Valued Logics
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ERCIM ManyVal Working Group

ManyVal is an ERCIM working group focusing on current hot topics inside the broad field of many-valued logics.

Many-valued logics

Many-valued logics are non-classical logics whose intended semantics have more than two truth-values. They were first studied in the early 20th century as a rather marginal topic in works by Lukasiewicz and Post on finitely-valued logics. In the past few decades, however, many-valued logics have gained more and more prominence, attracting an increasing number of researchers studying a growing family of logics arising from a broad range of motivations and yielding numerous applications.

Many-valued logics currently occupy a central part in the landscape of non-classical logics, including well-known systems such as Kleene logics, Dunn-Belnap logic and other bilattice-valued logics, n-valued Lukasiewicz logics, fuzzy logics (Lukasiewicz infinitely-valued logic, Gödel-Dummett logic and many others), paraconsistent logics, relevance logics, monoidal logic, etc.

Moreover, other systems such as intuitionistic, modal, or linear logic whose intended semantics is of a different nature, can also be given algebraic semantics with more than two truth values and hence, can be fruitfully studied from the point of view of Algebraic Logic as many-valued systems.

Research on this family of logics has benefited from connections with other mathematical disciplines such as universal algebra, topology, model theory, proof theory, game theory and category theory, and has resulted in many applications in fields across mathematics, philosophy and computer science.