Studia Logica 74 (1-2):275 - 311 (2003)
A category theoretic generalization of the theory of algebraizable deductive systems of Blok and Pigozzi is developed. The theory of institutions of Goguen and Burstall is used to provide the underlying framework which replaces and generalizes the universal algebraic framework based on the notion of a deductive system. The notion of a term -institution is introduced first. Then the notions of quasi-equivalence, strong quasi-equivalence and deductive equivalence are defined for -institutions. Necessary and sufficient conditions are given for the quasi-equivalence and the deductive equivalence of two term -institutions, based on the relationship between their categories of theories. The results carry over without any complications to institutions, via their associated -institutions. The -institution associated with a deductive system and the institution of equational logic are examined in some detail and serve to illustrate the general theory.
|Keywords||Algebraic Logic Multi-sorted Behavioral Logic Behavioral Algebraizability Behavioral Leibniz Operator Behavioral Leibniz Hierarchy Multi-sorted π-Institutions Behavioral Leibniz Congruence Systems Behavioral Categorical Leibniz Hierarchy|
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References found in this work BETA
Quasivarieties of Logic, Regularity Conditions and Parameterized Algebraization.G. D. Barbour & J. G. Raftery - 2003 - Studia Logica 74 (1-2):99 - 152.
Citations of this work BETA
Categorical Abstract Algebraic Logic: Referential Algebraic Semantics.George Voutsadakis - 2013 - Studia Logica 101 (4):849-899.
Categorical Abstract Algebraic Logic: The Largest Theory System Included in a Theory Family.George Voutsadakis - 2006 - Mathematical Logic Quarterly 52 (3):288-294.
Categorical Abstract Algebraic Logic: The Diagram and the Reduction Operator Lemmas.George Voutsadakis - 2007 - Mathematical Logic Quarterly 53 (2):147-161.
Multi‐Term Π‐Institutions and Their Equivalence.José Gil‐Férez - 2006 - Mathematical Logic Quarterly 52 (5):505-526.
Categorical Abstract Algebraic Logic: Gentzen Π ‐Institutions and the Deduction‐Detachment Property.George Voutsadakis - 2005 - Mathematical Logic Quarterly 51 (6):570-578.
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