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

• Autorzy: Voutsadakis G.

Identyfikatory

DOI

10.4467/20842589RM.17.004.7142

• Języki publikacji: EN

Abstrakty

EN

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

EN

sentential logics; logical matrices; implicative logics; Suszko congruence; π-Institutions; Wójcicki's conjecture; Malinowski's theorem

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2017
• Tom: Vol. 52
• Strony: 69--82
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Voutsadakis G.

• School of Mathematics and Computer Science Lake Superior State University Sault Sainte Marie, MI 49783, USA

Bibliografia

• [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 Wójcicki'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. Wójcicki, Matrix Approach in Methodology of Sentential Calculi, Studia Logica 32:1 (1973), 7-37.
• [8] G. Voutsadakis, Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity, 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

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).