Note: This book was later replaced by "A New Introduction to Modal Logic" (1996).
Modal logic can be described briefly as the logic of necessity and possibility, of 'must be' and 'may be'.
We had two main aims in writing this book. One was to explain in detail what modal logic is and how to do it; the other was to give a picture of the whole subject at the present stage of its development. The first of these aims dominates Part I, and to a lesser extent Part II; the second dominates Part III. Part I could be used on its own as a text-book for an introductory course of instruction on the basic theory and techniques of modal logic.
We have tried to make the book self-contained by including at the appropriate points summaries of all the non-modal logic we use in the exposition of the modal systems. It could therefore be tackled by someone who had not studied any logic at all before. To get the most out of it, however, such a reader would be well advised to buy himself another book on logic as well and to learn something more about the Propositional Calculus and the Lower Predicate Calculus than we have been able to tell him here.
Author(s): G. E. Hughes, M. J. Cresswell
Series: University Paperbacks, Volume 431
Publisher: Methuen
Year: 1972
Language: English
Pages: 403
Preface page ix
Note on References xi
Note to the Second Printing xi
PART I MODAL PROPOSITIONAL LOGIC
1 Non-modal Propositional Calculus 3
2 The System T 22
3 The Systems S4 and S5 43
4 Validity in T, S4 and S5 61
5 T: Decision Procedure and Completeness 82
6 S4 and S5: Decision Procedures and Completeness 105
7 Some Alternative Bases for T, S4 and S5 123
PART II MODAL PREDICATE LOGIC
8 The Lower Predicate Calculus 133
9 The Completeness of Modal LPC 149
10 Modality and Existence 170
11 Identity and Description in Modal LPC 189
PART III A SURVEY OF MODAL LOGIC
12 The Lewis Systems (I) 213
13 The Lewis Systems (II) 239
14 Other Modal Propositional Systems 255
15 Validity and Decision Procedures for Various Systems 274
16 Non-standard Systems 293
17 Boolean Algebra and Modal Logic 311
Appendix 1 Natural Deduction and Modal Systems 331
Appendix 2 Entailment and Strict Implication 335
Appendix 3 Axiomatic Bases for Propositional Modal
Systems 340
Appendix 4 Notation 347
Appendix 5 Kripke's Model Structures and Hintikka's
Model Sets 350
Solutions to Exercises 353
Bibliography 356
Index of Authors 373
Index of Subjects 377
List of Symbols and Important Rules 387
