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＜電子ブック＞
Proof Theory for Fuzzy Logics / by George Metcalfe, Nicola Olivetti, Dov M. Gabbay
(Applied Logic Series ; 36)

版	1st ed. 2009.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	VIII, 276 p : online resource
著者標目	*Metcalfe, George author Olivetti, Nicola author Gabbay, Dov M author SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Mathematics LCSH:Algebra LCSH:Artificial intelligence LCSH:Logic FREE:Mathematical Logic and Foundations FREE:Mathematics FREE:Algebra FREE:Artificial Intelligence FREE:Logic FREE:Order, Lattices, Ordered Algebraic Structures
一般注記	The Semantic Basis -- Hilbert Systems -- Gentzen Systems -- Syntactic Eliminations -- Fundamental Logics -- Uniformity and Efficiency -- First-Order Logics -- Further Topics 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 HTTP:URL=https://doi.org/10.1007/978-1-4020-9409-5

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