Equivalential logics (I)

Studia Logica 40 (3):227 - 236 (1981)
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The class of equivalential logics comprises all implicative logics in the sense of Rasiowa [9], Suszko's logicSCI and many Others. Roughly speaking, a logic is equivalential iff the greatest strict congruences in its matrices (models) are determined by polynomials. The present paper is the first part of the survey in which systematic investigations into this class of logics are undertaken. Using results given in [3] and general theorems from the theory of quasi-varieties of models [5] we give a characterization of all simpleC-matrices for any equivalential logicC (Theorem I.14). In corollaries we give necessary and sufficient conditions for the class of all simple models for a given equivalential logic to be closed under free products (Theorem I.18).



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Citations of this work

Protoalgebraic logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
Synonymous logics.Francis Jeffry Pelletier & Alasdair Urquhart - 2003 - Journal of Philosophical Logic 32 (3):259-285.
The Poset of All Logics II: Leibniz Classes and Hierarchy.R. Jansana & T. Moraschini - 2023 - Journal of Symbolic Logic 88 (1):324-362.
Equivalential logics (II).Janusz Czelakowski - 1981 - Studia Logica 40 (4):355 - 372.
Algebraic aspects of deduction theorems.Janusz Czelakowski - 1985 - Studia Logica 44 (4):369 - 387.

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References found in this work

An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.
Reduced products of logical matrices.Janusz Czelakowski - 1980 - Studia Logica 39 (1):19 - 43.

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