Categorical  Abstract  Algebraic  Logic: Referential π-Institutions

George Voutsadakis

doi:10.18778/0138-0680.44.1.2.05

Authors

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

DOI:

https://doi.org/10.18778/0138-0680.44.1.2.05

Keywords:

Referential Logics, Selfextensional Logics, Leibniz operator, Tarski operator, Suszko operator, π-institutions

Abstract

Wojcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of algebraic and matrix semantics of arbitrary sentential logics. A well-known theorem of Wojcicki asserts that a logic has a referential semantics if and only if it is selfextensional. Referential semantics was subsequently studied in detail by Malinowski and the concept of selfextensionality has played, more recently, an important role in the field of abstract algebraic logic in connection with the operator approach to algebraizability. We introduce and review some of the basic definitions and results pertaining to the referential semantics of π-institutions, abstracting corresponding results from the realm of propositional logics.

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