Dov M. Gabbay

George Metcalfe

Nicola Olivetti

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.

Proof Theory for Fuzzy Logics

Kai Brünnler

This book constitutes the refereed proceedings of the 20th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2011, held in Bern, Switzerland, in July 2011.The 16 revised research papers presented together with 2 system descriptions were carefully reviewed and selected from 34 submissions. The papers cover many topics in the wide range of applications of tableaux and related methods such as analytic tableaux for various logics, related techniques and concepts, related methods, new calculi and methods for theorem proving in classical and non-classical logics, as well as systems, tools, implementations and applications; all with a special focus on hardware and software verifications, semantic technologies, and knowledge engineering.

George Metcalfe

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