Logic for Applications

This book is a rigorous introduction to classical and nonclassical logics which emphasizes deduction as a form of computation. It can be used to teach classical, modal, and intuitistic predicate logic. It also presents the logical and mathematical foundations for resolution theorem proving and Logic Programming. A distinctive feature of this book is its uniform mathematical treatment of logic, based on the tableau method of classical logic, which includes soundness, completeness, compactness, incompleteness, and the theorems of Herb Rand and Skolem-L Wenheim. The same uniform treatment is used for important areas of application in computer science and artificial intelligence. These include resolution theorem proving, Logic Programming and Prolog, Predicate Intuitionistic Logic, and Predicate Modal Logic. There is also an historical appendix and an extensive list of selected references so that both the background and more advanced developments of these subjects can be understood and pursued. This text is appropriate for upper level undergraduate and beginning graduate students. In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the recent dramatic growth in the applications of logic to computer science. Thus our choice of topics has been heavily influenced by such applications. Of course, we cover the basic traditional topics - syntax, semantics, soundness, completeness and compactness - as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much of our book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic, especially in its application to Logic Programming and PROLOG. We deal extensively with the mathematical foundations of all three of these subjects. In addition, we include two chapters on nonclassical logic- modal and intuitionistic - that are becoming increasingly important in computer science. We develop the basic material on the syntax and se­ mantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method introduced for classical logic. We indicate how it can easily be adapted to various other special types of modal log­ ics. A number of more advanced topics (including nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG. "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."--Jacket Front Matter....Pages i-xvii Propositional Logic....Pages 1-71 Predicate Logic....Pages 73-144 Prolog....Pages 145-206 Modal Logic....Pages 207-245 Intuitionistic Logic....Pages 247-294 Back Matter....Pages 295-370 Contents: Propositional Logic Predicate Logic PROLOG Modal Logic Intuitionistic Logic Appendix A: An Historical Overview Appendix B: A Geneological Database.