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

George Voutsadakis


During the Autumn School on Strongly Finite Sentential Calculi held in Miedzygorze in 1977, Wojcicki 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 satis es a simple technical condition that we name the Wojcicki condition. Malinowski proved the conjecture in 1978. We revisit Malinowski's Theorem in the setting of logics formalized as -institutions.


[1] W.J. Blok and D. Pigozzi, Algebraizable Logics, Memoirs of the American Mathematical Society, Vol. 77, No. 396 (1989).
[2] J. Czelakowski, Reduced Products of Logical Matrices, Studia Logica 39 (1980), 19{43.
[3] J. Czelakowski, The Suszko Operator Part I, Studia Logica 74:1-2 (2003), 181{231.
[4] J.M. Font and R. Jansana, A General Algebraic Semantics for Sentential Logics, Lecture Notes in Logic, Vol. 332, No. 7 (1996), Springer-Verlag, Berlin Heidelberg, 1996.
[5] G. Malinowski, A Proof of Ryszard Wojcicki's Conjecture, Bulletin of the Section of Logic 7:1 (1978), 20{25.
[6] H. Rasiowa, An Algebraic Approach to Non-Classical Logics, Studies in Logic and the Foundations of Mathematics, Elsevier Science, 1974.
[7] R. Wojcicki, Matrix Approach in Methodology of Sentential Calculi, Studia Logica 32:1 (1973), 7{37.
[8] G. Voutsadakis, Categorical Abstract Algebraic Logic: Prealgebraicity and Protoal gebraicity, Studia Logica 85:2 (2007), 215{249.
[9] G. Voutsadakis, Categorical Abstract Algebraic Logic: The Subdirect Product Theorem, available in

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