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

George Voutsadakis

Abstrakt

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
References

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[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 http://www.voutsadakis.com/RESEARCH/papers.html

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