Equivalential logics

Studia Logica 40 (3):227-236 (1981)
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Abstract

The class of equivalential logics comprises all implicative logics in the sense of Rasiowa [9], Suszko's logic SCI and many others. Roughly speaking, a logic is equivalential iff the greatest strict congruences in its matrices 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 simple C-matrices for any equivalential logic C. 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.

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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.
Admissible Rules and the Leibniz Hierarchy.James G. Raftery - 2016 - Notre Dame Journal of Formal Logic 57 (4):569-606.
Equivalential Logics (II).Janusz Czelakowski - 1981 - Studia Logica 40 (4):355 - 372.

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