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Categorical abstract algebraic logic : Wójcicki's conjecture and Malinowski's theorem

Voutsadakis G.

Reports on Mathematical Logic

2017

Vol. 52

69--82

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.