The Semantic Foundations of Logic: Propositional Logics

This new edition of the author's well-received Propositional Logics presents the history, philosophy, and mathematics of its subject. Individual chapters are devoted to classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and analytic implication. Each chapter begins with a motivation in the originator's own terms, followed by the standard formal semantics and syntax, and completeness theorems. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations. This is the first book to unify many different logics within a common spectrum of semantic analysis: as the aspect of propositions under consideration varies, the logic varies. Translations between logics are analyzed--also for the first time-- along with necessary conditions for preserving meaning. In addition to logicians and philosophers, the book will interest computer scientists and linguists due to its clear explication of the relationship between mathematical semantics, formal languages, and natural languages, along with the flexible, simple methods of modeling reasoning provided by the general framework. This second edition includes worked examples and hundreds of new exercises, from routine to open problems, making it ideal for use in courses or for individual study.

Richard L. Epstein is at San Jose State University.