Deduction

"Deduction" is an efficient and elegant presentation of classical first-order logic. It presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague. Both are very natural and easy to learn. The definition of a formula excludes free variables, and the deduction system uses Show lines; the combination allows rules to be stated very simply. The book's main innovation is its final part, which contains chapters on extensions and revisions of classical logic: modal logic, many-valued logic, fuzzy logic, intuitionistic logic, counterfactuals, deontic logic, common-sense reasoning, and quantified modal logic. These have been areas of great logical and philosophical interest over the past 40 years, but few other textbooks treat them in any depth. "Deduction" makes these areas accessible to introductory students. All chapters have discussions of the underlying semantics and present both truth tree and deduction systems. New features in this edition, in addition to truth tree systems for classical and nonclassical logics, include new and simpler rules for modal logic, deontic logic, and counterfactuals; discussions of many-valued, fuzzy, and intuitionistic logics; an introduction to common-sense reasoning (nonmonotonic logic); and extensively reworked problem sets, designed to lead students gradually from easier to more difficult problems. This new edition also features web-based programs that make use of the book's methods. Each program is set up to give students symbolization problems, give them hints, grade their work, and do problems for them.