Authors:
- 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
Part of the book series: Applied Logic Series (APLS, volume 36)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
From the reviews:
"This is a pioneering book on proofs for fuzzy logics, well-suited both for logicians who are interested in fuzzy logic and for specialists in expert systems and fuzzy logic applications who want to know more about the applications of proof theory." (V. Ya. Kreinovich, Mathematical Reviews, Issue 2009 h)
“The class of mathematical fuzzy logics is a natural extension of the class of t-norm-based [0, 1]-valued logics. … the present monograph offers a study of proof-theoretically more interesting Gentzen-type calculi for such logics. … This monograph is a well readable and up-to-date presentation of its topic, which clearly indicates which interesting results have been proved … . It is excellently written by some of the leading experts in the field.” (Siegfried J. Gottwald, Zentralblatt MATH, Vol. 1168, 2009)Authors and Affiliations
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Department of Mathematics, Vanderbilt University, Nasville, USA
George Metcalfe
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Université Aix-Marseille III LSIS-UMR CNRS 6168, Avenue Escadrille Normandie-Niemen, France
Nicola Olivetti
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Department of Computer Science, King’s College, London, UK
Dov Gabbay
Bibliographic Information
Book Title: Proof Theory for Fuzzy Logics
Authors: George Metcalfe, Nicola Olivetti, Dov Gabbay
Series Title: Applied Logic Series
DOI: https://doi.org/10.1007/978-1-4020-9409-5
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2009
Hardcover ISBN: 978-1-4020-9408-8Published: 16 December 2008
Softcover ISBN: 978-90-481-8121-6Published: 22 October 2010
eBook ISBN: 978-1-4020-9409-5Published: 27 November 2008
Series ISSN: 1386-2790
Edition Number: 1
Number of Pages: VIII, 276
Topics: Mathematical Logic and Foundations, Mathematics, general, Algebra, Artificial Intelligence, Logic, Order, Lattices, Ordered Algebraic Structures