Matrices, primitive satisfaction and finitely based logics

Studia Logica 42 (1):89 - 104 (1983)
Abstract
We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.
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References found in this work BETA
Roman Suszko (1977). On Filters and Closure Systems. Bulletin of the Section of Logic 6 (4):151-154.
Piotr Wojtylak (1979). Entailment Relations and Matrices I. Bulletin of the Section of Logic 8 (2):112-115.
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