Categorical Abstract Algebraic Logic: Wojcicki's Conjecture and Malinowski's Theorem

George Voutsadakis


During the Autumn School on Strongly Finite Sentential Calculi held in Międzygórze in 1977, Wójcicki conjectured that a propositional logic has a strongly adequate matrix semantics consisting of matrices with a singleton designated filter, which we call a Rasiowa semantics since it is possessed by all implicative logics of Rasiowa, if and only if it satisfies a simple technical condition that we name the Wójcicki condition. Malinowski proved the conjecture in 1978. We revisit Malinowski's Theorem in the setting of logics formalized as π-institutions.

Słowa kluczowe: sentential logics, logical matrices, implicative logics, Suszko congruence, π-Institutions, Wójcicki’s conjecture, Malinowski’s theorem

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