A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an up-to-date and reliable guide essential for the student.
Author(s): Brian F. Chellas
Edition: 1
Publisher: Cambridge University Press
Year: 1980
Language: English
Pages: 305
Title ......Page 1
Copyright ......Page 2
Contents ......Page 3
Preface ......Page 7
PART I ......Page 9
1 Introduction ......Page 11
1.1 Truth and possible worlds ......Page 12
Exercises ......Page 18
1.2 The system S5 ......Page 22
Exercises ......Page 29
2.1 Syntax ......Page 33
Exercises ......Page 40
2.2 Models, truth, and validity ......Page 42
Exercises ......Page 47
2.3 Filtrations ......Page 49
Exercises ......Page 51
2.4 Systems of modal logic ......Page 53
Exercises ......Page 57
2.5 Axiomatizability ......Page 59
2.6 Maximality and Lindenbaum's lemma ......Page 61
2.7 Soundness, completeness, and canonical models ......Page 67
Exercises ......Page 69
2.8 Decidability and the finite model property ......Page 70
Exercises ......Page 72
PART II ......Page 73
3.1 Standard models ......Page 75
Exercises ......Page 79
3.2 The schemas D, T, B, 4, and 5 ......Page 84
Exercises ......Page 90
3.3 The schema G k,l,m,n ......Page 93
Exercises ......Page 98
3.4 Generated models ......Page 103
Exercises ......Page 106
3.5 Filtrations ......Page 108
Exercises ......Page 112
3.6 Filtrations, continued ......Page 113
Exercises ......Page 119
4 Normal systems of modal logic ......Page 121
4.1 Normal systems ......Page 122
Exercises ......Page 129
4.2 Replacement and duality ......Page 133
Exercises ......Page 138
4.3 The schemas D, T, B, 4, and 5 ......Page 139
Exercises ......Page 148
4.4 Modalities ......Page 155
Exercises ......Page 163
4.5 Maximal sets in normal systems ......Page 165
Exercises ......Page 168
5.1 Soundness ......Page 170
Exercises ......Page 173
5.2 Postscript on modalities ......Page 177
Exercises ......Page 178
5.3 Completeness: basic theorems ......Page 179
Exercises ......Page 182
5.4 Determination ......Page 183
Exercises ......Page 188
5.5 KG k,l,m,n ......Page 190
Exercises ......Page 193
5.6 Decidability ......Page 195
Exercises ......Page 197
6.1 Standard deontic logic ......Page 198
Exercises ......Page 200
6.2 Further principles ......Page 201
6.3 Obligation and time ......Page 203
6.4 Past tense obligation ......Page 206
6.5 Shortcomings ......Page 208
Exercises ......Page 210
PART III ......Page 213
7.1 Minimal models ......Page 215
Exercises ......Page 218
7.2 The schemas M, C, and N ......Page 222
Exercises ......Page 225
7.3 Augmentation ......Page 228
7.4 The schemas D, T, B, 4, and 5 ......Page 231
Exercises ......Page 233
7.5 Filtrations ......Page 235
Exercises ......Page 237
8.1 Classical systems ......Page 239
Exercises ......Page 241
8.2 Monotonic and regular systems ......Page 242
Exercises ......Page 248
8.3 Other schemas ......Page 253
Exercises ......Page 254
9.1 Soundness ......Page 256
Exercises ......Page 258
9.2 Completeness: basic theorems ......Page 260
Exercises ......Page 263
9.3 Determination ......Page 265
Exercises ......Page 268
9.4 The schemas D, T, B, 4, and 5 ......Page 269
9.5 Decidability ......Page 272
Exercises ......Page 274
10.1 Conditionality ......Page 276
Exercises ......Page 278
10.2 Conditional obligation ......Page 280
10.3 Conditional obligation defined ......Page 283
Exercises ......Page 284
Select bibliography ......Page 286
Index of symbols ......Page 289
Index of schemas, rules, and systems ......Page 291
Index of subjects ......Page 295
