Studia Logica 40 (3):227 - 236 (1981)
The class of equivalential logics comprises all implicative logics in the sense of Rasiowa , 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  and general theorems from the theory of quasi-varieties of models  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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References found in this work BETA
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
Matrix Approach in Methodology of Sentential Calculi.Ryszard Wójcicki - 1973 - Studia Logica 32 (1):7 - 39.
Some Theorems on Structural Consequence Operations.Stephen L. Bloom - 1975 - Studia Logica 34 (1):1 - 9.
On the Construction of Matrices Strongly Adequate for Pre-Finite Logics.Ewa Graczynska & Andrzej Wronski - 1974 - Bulletin of the Section of Logic 3 (2):15-17.
Citations of this work BETA
Categorical Abstract Algebraic Logic: Equivalent Institutions.George Voutsadakis - 2003 - Studia Logica 74 (1-2):275 - 311.
Logical Matrices and the Amalgamation Property.Janusz Czelakowski - 1982 - Studia Logica 41 (4):329 - 341.
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