Studia Logica 43 (4):353 - 377 (1984)

The present paper is thought as a formal study of distributive closure systems which arise in the domain of sentential logics. Special stress is laid on the notion of a C-filter, playing the role analogous to that of a congruence in universal algebra. A sentential logic C is called filter distributive if the lattice of C-filters in every algebra similar to the language of C is distributive. Theorem IV.2 in Section IV gives a method of axiomatization of those filter distributive logics for which the class Matr (C) prime of C-prime matrices (models) is axiomatizable. In Section V, the attention is focused on axiomatic strengthenings of filter distributive logics. The theorems placed there may be regarded, to some extent, as the matrix counterparts of Baker's well-known theorem from universal algebra [9, § 62, Theorem 2].
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DOI 10.1007/BF00370507
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References found in this work BETA

Equivalential Logics (I).Janusz Czelakowski - 1981 - Studia Logica 40 (3):227 - 236.
Reduced Products of Logical Matrices.Janusz Czelakowski - 1980 - Studia Logica 39 (1):19 - 43.

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Local Deductions Theorems.Janusz Czelakowski - 1986 - Studia Logica 45 (4):377 - 391.
Categorical Abstract Algebraic Logic: More on Protoalgebraicity.George Voutsadakis - 2006 - Notre Dame Journal of Formal Logic 47 (4):487-514.

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