Proof Theory for Fuzzy Logics

This accessible and up-to-date introduction to fuzzy logics focuses on the development and applications of "proof theoretic" presentations of fuzzy logics, including more than ten years of intensive work by researchers in that area.

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.

Provides a state-of-the-art introduction to fuzzy logics that is both accessible to researchers and students, and comprehensive, being the first book to take into account the many developments in the field of the past ten years Is the first book on proof theory for fuzzy logics, collecting together in one uniform and coherent presentation, previously widely dispersed results, methods, and applications in this area Provides a collection of easy-to-implement algorithms for logics widely used in Fuzzy Logic Provides a structured and uniform approach for designing and developing proof systems and establishing standard completeness for new logics that might interest or be useful to the reader Is the first book to present fuzzy logics in connection with well-known logics arising in different areas from Mathematics, Computer Science, and Philosophy, making it valuable for any reader with a broader interest in non-classical logics and automated reasoning

Inhalt
The Semantic Basis.- Hilbert Systems.- Gentzen Systems.- Syntactic Eliminations.- Fundamental Logics.- Uniformity and Efficiency.- First-Order Logics.- Further Topics.