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Categorical Abstract Algebraic Logic: Compatibility Operators and Correspondence Theorems

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Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 16))

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Abstract

Very recently Albuquerque, Font and Jansana, based on preceding work of Czelakowski on compatibility operators, introduced coherent compatibility operators and used Galois connections, formed by these operators, to provide a unified framework for the study of the Leibniz, the Suszko and the Tarski operators of abstract algebraic logic. Based on this work, we present a unified treatment of the operator approach to the categorical abstract algebraic logic hierarchy of π-institutions. This approach encompasses previous work by the author in this area, started under Don Pigozzi’s guidance, and provides resources for new results on the semantic, i.e., operator-based, side of the hierarchy.

To Don Pigozzi this work is dedicated

on the occasion of his 80th Birthday.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI, 49783, USA

    George Voutsadakis

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  1. George Voutsadakis
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Correspondence to George Voutsadakis .

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Editors and Affiliations

  1. Institute of Mathematics and Informatics, University of Opole, Opole, Poland

    Janusz Czelakowski

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Voutsadakis, G. (2018). Categorical Abstract Algebraic Logic: Compatibility Operators and Correspondence Theorems. In: Czelakowski, J. (eds) Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science. Outstanding Contributions to Logic, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-74772-9_15

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