Overview

This book considers both the algebraic and logical perspective within a common framework. It is written by experts in the area. It is easily accessible to graduate students and researchers from other fields. It features results summarized in tables and diagrams to provide an overview of the area. It is useful as a textbook for a course in algebraic logic, with exercises and suggested research directions. It provides a concise introduction to the subject and leads directly to research topics. The ideas from algebra and logic are developed hand-in-hand and the connections are shown in every level. This is a definitive book about residuated lattices and their connection with substructural logics. Although these fields originated independently in the early twentieth century, they are now, with the advent of algebraic logic, considered two sides of the same coin, and they have found numerous applications in, proof theory, algebra and computer science.; Substructural logics provide a uniform framework for classical logic, intuistionistic logic, relevance logics, fuzzy logics, linear logic and many other non-commutative versions of these, while residuated lattices include, among others, Boolean algebras, Heyting algebras, MV-algebras, basic logic algebras and lattice-ordered groups.

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9786611051068

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