Algebraization of quantifier logics, an introductory overview

Studia Logica 50 (3-4):485 - 569 (1991)
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Abstract

This paper is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics. The paper has a survey character, too. The most frequently used algebras like cylindric-, relation-, polyadic-, and quasi-polyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some directions we tried to give an overview of the most recent results and research trends, too.

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References found in this work

The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.
Cylindric Algebras. Part I.Leon Henkin, J. Donald Monk, Alfred Tarski, L. Henkin, J. D. Monk & A. Tarski - 1985 - Journal of Symbolic Logic 50 (1):234-237.
Cylindric Algebras. Part II.Leon Henkin, J. Donald Monk & Alfred Tarski - 1988 - Journal of Symbolic Logic 53 (2):651-653.
Algebraic Logic.Paul Richard Halmos - 2014 - New York, NY, USA: Chelsea.

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