Dynamic logic:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Mass. [u.a.]
MIT Press
2000
|
| Schriftenreihe: | Foundations of computing
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 459 S. graph. Darst. |
| ISBN: | 0262082896 |
Internformat
MARC
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| 245 | 1 | 0 | |a Dynamic logic |c David Harel ; Dexter Kozen ; Jerzy Tiuryn |
| 264 | 1 | |a Cambridge, Mass. [u.a.] |b MIT Press |c 2000 | |
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Datensatz im Suchindex
| _version_ | 1804128257258291200 |
|---|---|
| adam_text | Contents
Preface xiii
I FUNDAMENTAL CONCEPTS
1 Mathematical Preliminaries 3
1.1 Notational Conventions 3
1.2 Sets 3
1.3 Relations 5
1.4 Graphs and Dags 13
1.5 Lattices 13
1.6 Transfinite Ordinals 13
1.7 Set Operators 16
1.8 Bibliographical Notes 22
Exercises 22
2 Computability and Complexity 27
2.1 Machine Models 27
2.2 Complexity Classes 38
2.3 Reducibility and Completeness 53
2.4 Bibliographical Notes 63
Exercises 64
3 Logic 67
3.1 What is Logic? 67
3.2 Propositional Logic 71
3.3 Equational Logic 86
3.4 Predicate Logic 102
3.5 Ehrenfeucht Frai sse Games 119
3.6 Infinitary Logic 120
3.7 Modal Logic 127
3.8 Bibliographical Notes 134
viii Contents
Exercises 134
4 Reasoning About Programs 145
4.1 What are Programs? 145
4.2 States and Executions 146
4.3 Programming Constructs 147
4.4 Program Verification 152
4.5 Exogenous and Endogenous Logics 157
4.6 Bibliographical Notes 157
Exercises 158
II PROPOSITIONAL DYNAMIC LOGIC
5 Propositional Dynamic Logic 163
5.1 Syntax 164
5.2 Semantics 167
5.3 Computation Sequences 170
5.4 Satisfiability and Validity 171
5.5 A Deductive System 173
5.6 Basic Properties 174
5.7 Encoding Hoare Logic 186
5.8 Bibliographical Notes 187
Exercises 188
6 Filtration and Decidability 191
6.1 The Fischer Ladner Closure 191
6.2 Filtration and the Small Model Theorem 195
6.3 Filtration over Nonstandard Models 199
6.4 Bibliographical Notes 201
Exercises 202
7 Deductive Completeness 203
Contents ix
7.1 Deductive Completeness 203
7.2 Logical Consequences 209
7.3 Bibliographical Notes 209
Exercises 209
8 Complexity of PDL 211
8.1 A Deterministic Exponential Time Algorithm 211
8.2 A Lower Bound ¦ 216
8.3 Compactness and Logical Consequences 220
8.4 Bibliographical Notes 224
Exercises 225
9 Nonregular PDL 227
9.1 Context Free Programs 227
9.2 Basic Results 228
9.3 Undecidable Extensions 232
9.4 Decidable Extensions 237
9.5 More on One Letter Programs 250
9.6 Bibliographical Notes 255
Exercises 256
10 Other Variants of PDL 259
10.1 Deterministic PDL and While Programs 259
10.2 Restricted Tests 263
10.3 Representation by Automata 266
10.4 Complementation and Intersection 268
10.5 Converse 270
10.6 Well Foundedness and Total Correctness 271
10.7 Concurrency and Communication 276
10.8 Bibliographical Notes 277
x Contents
III FIRST ORDER DYNAMIC LOGIC
11 First Order Dynamic Logic 283
11.1 Basic Syntax 283
11.2 Richer Programs 287
11.3 Semantics 291
11.4 Satisfiability and Validity 297
11.5 Bibliographical Notes 298
Exercises 298
12 Relationships with Static Logics 301
12.1 The Uninterpreted Level 301
12.2 The Interpreted Level 307
12.3 Bibliographical Notes 311
Exercises 311
13 Complexity 313
13.1 The Validity Problem 313
13.2 Spectral Complexity 317
13.3 Bibliographical Notes 324
Exercises 325
14 Axiomatization 327
14.1 The Uninterpreted Level 327
14.2 The Interpreted Level 333
14.3 Bibliographical Notes 341
Exercises 341
15 Expressive Power 343
15.1 The Unwind Property 344
15.2 Spectra and Expressive Power 347
15.3 Bounded Nondeterminism 355
Contents xi
15.4 Unbounded Memory 369
15.5 The Power of a Boolean Stack 376
15.6 Unbounded Nondeterminism 377
15.7 Bibliographical Notes 378
Exercises 380
16 Variants of DL 383
16.1 Algorithmic Logic 383
16.2 Nonstandard Dynamic Logic 384
16.3 Well Foundedness 386
16.4 Dynamic Algebra 389
16.5 Probabilistic Programs 391
16.6 Concurrency and Communication 393
16.7 Bibliographical Notes 394
17 Other Approaches 397
17.1 Logic of Effective Definitions 397
17.2 Temporal Logic 398
17.3 Process Logic 408
17.4 The /x Calculus 415
17.5 Kleene Algebra 418
References 425
Notation and Abbreviations 439
Index 449
|
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| language | English |
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| spelling | Harel, David 1950- Verfasser (DE-588)109527992 aut Dynamic logic David Harel ; Dexter Kozen ; Jerzy Tiuryn Cambridge, Mass. [u.a.] MIT Press 2000 XV, 459 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Foundations of computing Dynamische modellen gtt Informatica gtt Logica gtt Logique informatique Logisch programmeren gtt Méthodes formelles (Informatique) Wiskundige modellen gtt Logik Computer logic Formal methods (Computer science) Dynamische Logik (DE-588)4637784-0 gnd rswk-swf Dynamische Logik (DE-588)4637784-0 s DE-604 Kozen, Dexter 1951- Verfasser (DE-588)135740436 aut Tiuryn, Jerzy Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009190986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harel, David 1950- Kozen, Dexter 1951- Tiuryn, Jerzy Dynamic logic Dynamische modellen gtt Informatica gtt Logica gtt Logique informatique Logisch programmeren gtt Méthodes formelles (Informatique) Wiskundige modellen gtt Logik Computer logic Formal methods (Computer science) Dynamische Logik (DE-588)4637784-0 gnd |
| subject_GND | (DE-588)4637784-0 |
| title | Dynamic logic |
| title_auth | Dynamic logic |
| title_exact_search | Dynamic logic |
| title_full | Dynamic logic David Harel ; Dexter Kozen ; Jerzy Tiuryn |
| title_fullStr | Dynamic logic David Harel ; Dexter Kozen ; Jerzy Tiuryn |
| title_full_unstemmed | Dynamic logic David Harel ; Dexter Kozen ; Jerzy Tiuryn |
| title_short | Dynamic logic |
| title_sort | dynamic logic |
| topic | Dynamische modellen gtt Informatica gtt Logica gtt Logique informatique Logisch programmeren gtt Méthodes formelles (Informatique) Wiskundige modellen gtt Logik Computer logic Formal methods (Computer science) Dynamische Logik (DE-588)4637784-0 gnd |
| topic_facet | Dynamische modellen Informatica Logica Logique informatique Logisch programmeren Méthodes formelles (Informatique) Wiskundige modellen Logik Computer logic Formal methods (Computer science) Dynamische Logik |
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