Categorical Abstract Algebraic Logic: Models of π-Institutions

Categorical Abstract Algebraic Logic: Models of π-Institutions

George Voutsadakis

Source: Notre Dame J. Formal Logic Volume 46, Number 4 (2005), 439-460.

Abstract

An important part of the theory of algebraizable sentential logics consists of studying the algebraic semantics of these logics. As developed by Czelakowski, Blok, and Pigozzi and Font and Jansana, among others, it includes studying the properties of logical matrices serving as models of deductive systems and the properties of abstract logics serving as models of sentential logics. The present paper contributes to the development of the categorical theory by abstracting some of these model theoretic aspects and results from the level of sentential logics to the level of π-institutions.

Primary Subjects: 03Gxx

Secondary Subjects: 18Axx, 68N05

Keywords: abstract algebraic logic; deductive systems; institutions; equivalent deductive systems; algebraizable deductive systems; adjunctions; equivalent institutions; algebraizable institutions; Leibniz congruence; Tarski congruence; algebraizable sentential logics

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1134397662
Digital Object Identifier: doi:10.1305/ndjfl/1134397662
Mathematical Reviews number (MathSciNet): MR2183054
Zentralblatt MATH identifier: 1089.03058

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