‎Proof Theory for Fuzzy Logics

Dordrecht, Netherland: Springer (2008)
  Copy   BIBTEX

Abstract

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 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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On Theories and Models in Fuzzy Predicate Logics.Petr Hájek & Petr Cintula - 2006 - Journal of Symbolic Logic 71 (3):863 - 880.
Logics with disjunction and proof by cases.San-min Wang & Petr Cintula - 2008 - Archive for Mathematical Logic 47 (5):435-446.
Adaptive fuzzy logics for contextual hedge interpretation.Stephan der Waart van Gulivank - 2009 - Journal of Logic, Language and Information 18 (3).
Adaptive fuzzy logics for contextual hedge interpretation.Stephan van der Waart van Gulik - 2009 - Journal of Logic, Language and Information 18 (3):333-356.
Mathematical fuzzy logics.Siegfried Gottwald - 2008 - Bulletin of Symbolic Logic 14 (2):210-239.
Structural Completeness in Fuzzy Logics.Petr Cintula & George Metcalfe - 2009 - Notre Dame Journal of Formal Logic 50 (2):153-182.
Advances in the ŁΠ and logics.Petr Cintula - 2003 - Archive for Mathematical Logic 42 (5):449-468.
Weakly Implicative (Fuzzy) Logics I: Basic Properties. [REVIEW]Petr Cintula - 2006 - Archive for Mathematical Logic 45 (6):673-704.
On the algebraic structure of linear, relevance, and fuzzy logics.Francesco Paoli - 2002 - Archive for Mathematical Logic 41 (2):107-121.

Analytics

Added to PP
2021-11-17

Downloads
12 (#929,749)

6 months
7 (#176,166)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Dov Gabbay
Hebrew University of Jerusalem

Citations of this work

A novel approach to equality.Andrzej Indrzejczak - 2021 - Synthese 199 (1-2):4749-4774.
Free Logics are Cut-Free.Andrzej Indrzejczak - 2021 - Studia Logica 109 (4):859-886.
Many-valued logic.Siegfried Gottwald - 2008 - Stanford Encyclopedia of Philosophy.

View all 11 citations / Add more citations

References found in this work

The logic of inexact concepts.J. A. Goguen - 1969 - Synthese 19 (3-4):325-373.
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
A theorem about infinite-valued sentential logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.
Fuzzy Sets.Lofti A. Zadeh - 1965 - Information and Control 8 (1):338--53.

View all 10 references / Add more references