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 analysed--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.

From reviews of the first edition: "Of the technical books I have read, it is one of the few that succeeds in presenting its material in a somewhat conversational style, which helps in understanding the author's point of view.... I would highly recommend this book to not only readers like myself who have an active growing interest in logic, but also to the more professional mathematician/computer scientist who has a deep working knowledge of current logic theory. Both groups, in my opinion, would profit from being exposed to Epstein's theory." --W. Truszkowski, SIGART Bulletin"Chapter 9 on translation between logics ...is perhaps the most interesting chapter of the book. Two great advantages of the book... are its readability and broad scope." --Journal of Logic and Computation"Throughout, treatment is thorough and the writing is clear. Superb bibliography; glossary; extensive index. Highly recommended for every specialist in logic." --Choice"Propositional Logics portray[s] both the breadth and depths to be found in this aspect of logic, too easily taken for granted. . . .Propositional Logics contains something for the mathematicians and something for the philosophers, something for the novices and something for the more experienced. The exercises in particular exemplify this breadth as they range from review questions (such as "What is a truth-functional connective?") to open problems. . .And many of the exercises are interesting in an offbeat way, such as "Formalize two theorems (principles) from a mathematics textbook, a biology textbook, a psychology textbook, and an economics textbook." . . .an interesting and insighful volume."--Modern Logic"Libraries which hope to offer opportunities for logical research need this book." --Mathematical ReviewsFrom reviews of the first edition: "The author tries to explain everything in simple language. Another prime feature is the large number of examples of translation from English into the logical formalism. Great care is taken in explaining background assumptions."--Mathematical Reviews..".an interesting and insightful volume."--Modern Logic From reviews of the first edition: "Of the technical books I have read, it is one of the few that succeeds in presenting its material in a somewhat conversational style, which helps in understanding the author's point of view.... I would highly recommend this book to not only readers like myself who have an active growing interest in logic, but also to the more professional mathematician/computer scientist who has a deep working knowledge of current logic theory. Both groups, in my opinion, would profit from being exposed to Epstein's theory." --W. Truszkowski, SIGART Bulletin "Chapter 9 on translation between logics ...is perhaps the most interesting chapter of the book. Two great advantages of the book... are its readability and broad scope." --Journal of Logic and Computation "Throughout, treatment is thorough and the writing is clear. Superb bibliography; glossary; extensive index. Highly recommended for every specialist in logic." --Choice "Propositional Logics portray[s] both the breadth and depths to be found in this aspect of logic, too easily taken for granted. . . .Propositional Logics contains something for the mathematicians and something for the philosophers, something for the novices and something for the more experienced. The exercises in particular exemplify this breadth as they range from review questions (such as "What is a truth-functional connective?") to open problems. . .And many of the exercises are interesting in an offbeat way, such as "Formalize two theorems (principles) from a mathematics textbook, a biology textbook, a psychology textbook, and an economics textbook," . . .an interesting and insighful volume."--Modern Logic "Librarieswhich hope to offer opportunities for logical research need this book." --Mathematical Reviews From reviews of the first edition: "The author tries to explain everything in simple language. Another prime feature is the large number of examples of translation from English into the logical formalism. Great care is taken in explaining background assumptions."--Mathematical Reviews,.".an interesting and insightful volume."--Modern Logic From reviews of the first edition: "Of the technical books I have read, it is one of the few that succeeds in presenting its material in a somewhat conversational style, which helps in understanding the author's point of view.... I would highly recommend this book to not only readers like myselfwho have an active growing interest in logic, but also to the more professional mathematician/computer scientist who has a deep working knowledge of current logic theory. Both groups, in my opinion, would profit from being exposed to Epstein's theory." --W. Truszkowski, SIGART Bulletin"Chapter 9 on translation between logics ...is perhaps the most interesting chapter of the book. Two great advantages of the book... are its readability and broad scope." --Journal of Logic and Computation"Throughout, treatment is thorough and the writing is clear. Superb bibliography; glossary; extensive index. Highly recommended for every specialist in logic." --Choice"Propositional Logics portray[s] both the breadth and depths to be found in this aspect of logic, too easily taken for granted. . . .Propositional Logics contains something for the mathematicians and something for the philosophers, something for the novices and something for the more experienced.The exercises in particular exemplify this breadth as they range from review questions (such as "What is a truth-functional connective?") to open problems. . .And many of the exercises are interesting in an offbeat way, such as "Formalize two theorems (principles) from a mathematics textbook, abiology textbook, a psychology textbook, and an economics textbook," . . .an interesting and insighful volume."--Modern Logic"Librarieswhich hope to offer opportunities for logical research need this book." --Mathematical ReviewsFrom reviews of the first edition: "The author tries to explain everything in simple language. Another prime feature is the large number of examples of translation from English into the logical formalism. Great care is taken in explaining background assumptions."--Mathematical Reviews,.".an interesting and insightful volume."--Modern Logic