Beyond Rasiowa's Algebraic Approach to Non-classical Logics

Studia Logica 82 (2):179-209 (2006)
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This paper reviews the impact of Rasiowa's well-known book on the evolution of algebraic logic during the last thirty or forty years. It starts with some comments on the importance and influence of this book, highlighting some of the reasons for this influence, and some of its key points, mathematically speaking, concerning the general theory of algebraic logic, a theory nowadays called Abstract Algebraic Logic. Then, a consideration of the diverse ways in which these key points can be generalized allows us to survey some issues in the development of the field in the last twenty to thirty years. The last part of the paper reviews some recent lines of research that in some way transcend Rasiowa's approach. I hope in this way to give the reader a general view of Rasiowa's key position in the evolution of Algebraic Logic during the twentieth century.



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Complete additivity and modal incompleteness.Wesley H. Holliday & Tadeusz Litak - 2019 - Review of Symbolic Logic 12 (3):487-535.
The simplest protoalgebraic logic.Josep Maria Font - 2013 - Mathematical Logic Quarterly 59 (6):435-451.

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References found in this work

The completeness of the first-order functional calculus.Leon Henkin - 1949 - Journal of Symbolic Logic 14 (3):159-166.
A survey of abstract algebraic logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Protoalgebraic logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
Equivalence of Consequence Operations.W. J. Blok & Bjarni Jónsson - 2006 - Studia Logica 83 (1-3):91-110.

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