Logic for Applications (Texts & Monographs in Computer Science)

Logic for Applications presents a rigorous introduction to classical, intuitionistic, and modal logic. The book emphasizes deduction as a form of computation by examining the logical and mathematical foundations of resolution theorem proving and logic programming. These subjects are important for many areas of applications in computer science and artificial intelligence. Topics covered include soundness, completeness, and undecidability for classical, nonclassical, and computation-based logical systems as well as compactness and the theorems of Herbrand and Skolem-Lowenheim. In context of PROLOG, termination conditions, negation as failure, and the relations to nonmonotonic logic are all discussed.
This book is an ideal textbook for presenting classical and non-classical logic as well as logic programming to advanced undergraduate or beginning graduate students in computer science or mathematics. It contains a historical appendix and an extensive list of references for further studies in the field. No advanced mathematical background is required.

This textbook provides a first introduction to mathematical logic which is closely attuned to the applications of logic in computer science. In it the authors emphasize the notion that deduction is a form of computation. While all the traditional subjects of logic are covered thoroughly - syntax, semantics, completeness, and compactness - much of the book deals with less traditional topics such as resolution theorem proving, logic programming, and non-classical logics - modal and intuitionistic - which are becoming increasingly important in computer science. The book also provides a systematic treatment of the elements of set theory, a historical overview of its subjects, and an extensive annotated bibliography. No previous exposure to logic is assumed, and so this will be suitable for upper level undergraduate or beginning graduate students in computer science or mathematics.