Universal Algebraic Logic

Beschreibung

This book connects logic with algebra. It covers universal logic and the question of what logic is as well as universal algebraic logic and duality theories between the world of logics and the world of algebra. It also discusses algebraic logic proper including algebras of relations of various ranks, Tarski's cylindric algebras, relation algebras, Halmos' polyadic algebras and other kinds of algebras of logic.

The three main themes of this book are (i) universal logic and the question of what logic is, (ii) universal algebraic logic and duality theories between the world of logics and the world of algebra, and (iii) algebraic logic proper including algebras of relations of various ranks, Tarski's cylindric algebras, relation algebras, Halmos' polyadic algebras and other kinds of algebras of logic. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. An introductory chapter contains the necessary algebraic basics, this can be used in its own right as a quick introduction to universal algebra.

Autor*in

Hajnal Andréka

Themen in »Universal Algebraic Logic«

Cylindric algebras Denotation Duality theories Lindström-type theorems Logic with semantics Logic, algebra, geometry triad Meaning algebras Semantical algebraizable logics Spacetime geometries Syntax-semantics duality Universal Logic

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