A New Introduction to Modal Logic

Modal logic is the logic of necessity and possibility, of 'must be' and 'may be'. Unlike non-modal logic, it codifies structures which represent how things could be as well as how things are. This book is intended to replace the widely used Introduction to Modal Logic and the more recent, Companion to Modal Logic , by the same authors. The principle changes include the incorporation of developments that have taken place since 1968 both in modal propositional logic and in modal predicate logic, but without sacrificing the clarity of exposition and the accessiblity of the material which were essential features of the earlier books. Most importantly, the book has been completely rewritten and in no sense is a 'new edition' of either book. A New Introduction to Modal Logic guides readers through the most basic systems of modal predicate logic with identity. It deals with both technical developments such as completeness and incompleteness, and finite and infinite models, and discusses philosophical applications, especially in the area of predicate logic. Written for students of logic and for their lecturers, philosophers, linguistics, mathematicians, computer scientists and those studying cognitive science or semantics. A New Introduction to Modal Logic is the only textbook you will need.

Table of Contents:
Preface, Part One: Basic Modal Propositional Logic, 1. The Basic Notions, 2. The Systems K, T and D, 3. The Systems S4, S5, B, Triv and Ver, 4. Testing for validity, 5. Conjunctive Normal Form, 6. Completeness, Part Two: Normal Modal Systems, 7. Canonical Models, 8. Finite Models, 9. Incompleteness, 10. Frames and Systems, 11. Strict Implication, 12. Glimpses Beyond, Part Three: Modal Predicate Logic, 13. The Lower Predicate Calculus, 14. The Completeness of Modal LPC, 15. Expanding Domains, 16. Modality and Existence, 17. Identity and Descriptions, 18. Intensional Objects, 19. Further Issues, Axioms, Rules and Systems, Solutions to Selected Exercises, Bibliography, Index

Review :
"There has long been a need for a new version, and this is a superb new version. The new Hughes and Cresswell would clearly be the text of choice for introductory courses in modal logic. I expect this would be a standard reference in the subject for some years to come.." -Michael Byrd, University of Wisconsin-Madison "Written ... with great pedagogical skill, [An Introduction to Modal Logic] can be recommended to all those (especially without a solid mathematical background) who want to make the first acquaintance with the subject." -"Journal of Symbolic Logic "[T]his new presentation on modal logic provides a much-needed updating of the [authors' earlier]classic introduction which preserves all the virtues of the original, but responds to all the advances in modal logic which are appropriate to its introductory nature. It is the new classic introductory text on modal logic." -"Studia Logica