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2006 Categorical Abstract Algebraic Logic: More on Protoalgebraicity
George Voutsadakis
Notre Dame J. Formal Logic 47(4): 487-514 (2006). DOI: 10.1305/ndjfl/1168352663


Protoalgebraic logics are characterized by the monotonicity of the Leibniz operator on their theory lattices and are at the lower end of the Leibniz hierarchy of abstract algebraic logic. They have been shown to be the most primitive among those logics with a strong enough algebraic character to be amenable to algebraic study techniques. Protoalgebraic π-institutions were introduced recently as an analog of protoalgebraic sentential logics with the goal of extending the Leibniz hierarchy from the sentential framework to the π-institution framework. Many properties of protoalgebraic logics, studied in the sentential logic framework by Blok and Pigozzi, Czelakowski, and Font and Jansana, among others, have already been adapted in previous work by the author to the categorical level. This work aims at further advancing that study by exploring in this new level some more properties of protoalgebraic sentential logics.


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George Voutsadakis. "Categorical Abstract Algebraic Logic: More on Protoalgebraicity." Notre Dame J. Formal Logic 47 (4) 487 - 514, 2006.


Published: 2006
First available in Project Euclid: 9 January 2007

zbMATH: 1134.03044
MathSciNet: MR2272084
Digital Object Identifier: 10.1305/ndjfl/1168352663

Primary: 03G99
Secondary: 18C15 , 68N30

Keywords: adjunctions , algebraic logic , algebraizable deductive systems , algebraizable institutions , equivalent categories , equivalent deductive systems , equivalent institutions , equivalential logics , Leibniz hierarchy , Leibniz operator , protoalgebraic logics , Tarski operator

Rights: Copyright © 2006 University of Notre Dame

Vol.47 • No. 4 • 2006
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