Archive for Mathematical Logic 45 (6):673-704 (2006)

Abstract
This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass–the class of weakly implicative fuzzy logics. It contains the majority of logics studied in the literature under the name fuzzy logic. We present many general theorems for both classes, demonstrating their usefulness and importance
Keywords Implicative logic  Fuzzy logic  Consequence relation  Matrix semantics
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DOI 10.1007/s00153-006-0011-5
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References found in this work BETA

An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.
A Survey of Abstract Algebraic Logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Protoalgebraic Logics.Janusz Czelakowski - 2001 - Kluwer Academic Publishers.
Algebraic Methods in Philosophical Logic.J. Michael Dunn - 2001 - Oxford, England: Oxford University Press.

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Citations of this work BETA

On Theories and Models in Fuzzy Predicate Logics.Petr Hájek & Petr Cintula - 2006 - Journal of Symbolic Logic 71 (3):863 - 880.
On Vagueness, Truth Values and Fuzzy Logics.Petr Hájek - 2009 - Studia Logica 91 (3):367-382.

View all 22 citations / Add more citations

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