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2015 Categorical Abstract Algebraic Logic: Truth-Equational π-Institutions
George Voutsadakis
Notre Dame J. Formal Logic 56(2): 351-378 (2015). DOI: 10.1215/00294527-2864343


Finitely algebraizable deductive systems were introduced by Blok and Pigozzi to capture the essential properties of those deductive systems that are very tightly connected to quasivarieties of universal algebras. They include the equivalential logics of Czelakowski. Based on Blok and Pigozzi’s work, Herrmann defined algebraizable deductive systems. These are the equivalential deductive systems that are also truth-equational, in the sense that the truth predicate of the class of their reduced matrix models is explicitly definable by some set of unary equations. Raftery undertook the task of characterizing the property of truth-equationality for arbitrary deductive systems. In this paper, following Raftery, we extend the notion of truth-equationality for logics formalized as π-institutions and abstract several of the results that hold for deductive systems in this more general categorical context.


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George Voutsadakis. "Categorical Abstract Algebraic Logic: Truth-Equational π-Institutions." Notre Dame J. Formal Logic 56 (2) 351 - 378, 2015.


Published: 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1333.03269
MathSciNet: MR3337385
Digital Object Identifier: 10.1215/00294527-2864343

Primary: 03G27

Keywords: algebraizable logics , deductive system , Leibniz congruence , logical matrix , Suszko congruence , truth-equational logics

Rights: Copyright © 2015 University of Notre Dame

Vol.56 • No. 2 • 2015
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