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.