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This long-awaited book replaces not one but both of Hughes and Cresswell's two previous classic studies of modal logic: "An Introduction to Modal Logic" and "A Companion to Modal Logic." "A New Introduction to Modal Logic" has been completely rewritten by the authors to incorporate all the developments that have taken place since 1968 both in modal propositional logical and modal predicate logic, but without sacrificing the clarity of exposition and approachability that were essential features of the earlier works. The book takes readers through the most basic systems of modal prepositional logic right up to systems of modal predicate 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 modal predicate logic.
M.J. Cresswell, G.E. Hughes
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
