Richard L. Epstein
Propositional Logics presents the history, philosophy, and mathematics of the major systems of propositional logic.
Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and analytic implication are examined in separate chapters. Each begins with a motivation in the originators’ 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 of the logics.
The view that unifies the exposition is that propositional logics comprise a spectrum. As the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A general theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning.
The analysis of the relationship between formal mathematical semantics, formal languages, and natural languages, along with the flexible, simple methods of modeling reasoning provided by the general framework will be of special interest to computer scientists and linguists.
For this third edition the material has been re-organized to make the exposition easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations.
The text includes worked examples and hundreds of homework exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.
"Highly recommended for every specialist in logic ... Treatment is thorough and the writing is clear." — Choice
"Epstein writes well, in a relaxed style. His unifying perspective of propositional logic, discussions of individual logics, and often thought-provoking exercises all make for an interesting and insightful volume." — Modern Logic
"Interesting and very readable. I particularly like the way this book combines the presentation of rather technical material with stimulating philosophical discussions. It is also an important book ... it covers in one volume basic technical information, on an undergraduate level, about a variety of propositional logics [and]it attempts to clarify the foundations of logic and to solve the crucial problem: 'What is a logic?'" — Journal of Logic and Computation