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Algebraic logic --- Logique algébrique

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The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has considerable mathematical significance, with applications in various fields: e.g., in computer science---databases, specification theory, AI---and in anthropology, economics, physics, and philosophical logic.This comprehensive treatment of the theory of relation algebras and the calculus of relations is the first devoted to a systematic development of the subject.Key Features:- Presents historical milestones from a modern perspecti

Relation algebras. --- Algebra of relations --- Algebras, Relation --- Relational algebras --- Relations, Algebra of --- Algebraic logic --- Algebraic logic.

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In a bold and refreshingly informal style, this exciting text steers a middle course between elementary texts emphasizing connections with philosophy, logic, and electronic circuit design, and profound treatises aimed at advanced graduate students and professional mathematicians. It is written for readers who have studied at least two years of college-level mathematics. With carefully crafted prose, lucid explanations, and illuminating insights, it guides students to some of the deeper results of Boolean algebra --- and in particular to the important interconnections with topology --- without assuming a background in algebra, topology, and set theory. The parts of those subjects that are needed to understand the material are developed within the text itself. Highlights of the book include the normal form theorem; the homomorphism extension theorem; the isomorphism theorem for countable atomless Boolean algebras; the maximal ideal theorem; the celebrated Stone representation theorem; the existence and uniqueness theorems for canonical extensions and completions; Tarski’s isomorphism of factors theorem for countably complete Boolean algebras, and Hanf’s related counterexamples; and an extensive treatment of the algebraic-topological duality, including the duality between ideals and open sets, homomorphisms and continuous functions, subalgebras and quotient spaces, and direct products and Stone-Cech compactifications. A special feature of the book is the large number of exercises of varying levels of difficulty, from routine problems that help readers understand the basic definitions and theorems, to intermediate problems that extend or enrich material developed in the text, to harder problems that explore important ideas either not treated in the text, or that go substantially beyond its treatment. Hints for the solutions to the harder problems are given in an appendix. A detailed solutions manual for all exercises is available for instructors who adopt the text for a course.

Algebra, Boolean. --- Algebraic logic. --- Logic, Symbolic and mathematical --- Boolean algebra --- Boole's algebra --- Algebraic logic --- Set theory --- Booleaanse algebra. --- Boolesche Algebra. --- Boole, Algèbre de

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Algebraic logic. --- Probabilities. --- Algebraic logic --- Probabilities --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Logic, Symbolic and mathematical --- Logique algébrique --- Probabilités

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Algebra, Boolean --- Boolean algebra --- Boole's algebra --- Algebraic logic --- Set theory