Proof methods for modal and intuitionistic logics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Reidel
1983
|
| Series: | Synthese library
169 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 555 S. |
| ISBN: | 9027715734 |
Staff View
MARC
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
INTRODUCTION 1
CHAPTER ONE/BACKGROUND
1. Propositional Formulas 11
2. Models 14
3. A Unifying Notation 22
4. Classical Semantic Tableaus 29
CHAPTER TWO / ANALYTIC MODAL TABLEAUS AND
CONSISTENCY PROPERTIES
1. Tableau Rules for K, K4, T, S4, D and D4 33
2. Uniform Modal Notation 41
3. Correctness 43
4. A Note on Completeness Proofs 46
5. Consistency Properties for K, K4, T, S4, D and D4 48
6. Tableau Completeness 60
CHAPTER THREE / LOGICAL CONSEQUENCE, COMPACTNESS,
INTERPOLATION, AND OTHER TOPICS
1. Introduction 64
2. Logical Consequence 65
3. Strong Tableau Completeness 70
4. Compactness Theorems 74
5. The Deduction Theorem 77
6. Gentzen Systems 81
7. Symmetric Gentzen Systems 88
8. The Craig Interpolation Lemma 93
9. Other Interpolation Theorems 99
10. The Beth Definability Theorem 105
11. Further Consequences of Interpolation Theorems 110
12. Decidability 115
v
vi TABLE OF CONTENTS
CHAPTER FOUR / AXIOM SYSTEMS AND NATURAL
DEDUCTION
1. Introduction 118
2. A Classical Propositional Axiom System 118
3. An Underlying Modal Logic 123
4. Results about the Logic U 127
5. The Logic K Axiomatized 130
6. Correctness and Completeness of the K Axiomatization 134
7. The Logics K4, T, S4, D and D4 Axiomatization 137
8. Finite Axiomatizability, Part I 141
9. Finite Axiomatizability, Part II 148
10. A Classical Natural Deduction System 153
11. Some Results about Natural Deduction 162
12. A Note on Modal Natural Deduction Rules 170
13. I style Natural Deduction Rules 171
14. I style Completeness and Correctness 176
15. A style Natural Deduction Rules 184
16. A style Completeness and Correctness 187
CHAPTER FIVE / NON ANALYTIC LOGICS
1. Introduction 191
2. Synthetic KB, DB, B and S5 Tableaus 193
3. Semi analytic KB, DB, B and S5 Tableaus 201
4. Consistency Properties for KB, DB, B and S5 205
5. Immediate Consequences 209
6. KB, DB, B and S5 Axiomatized 210
7. Natural Deduction for KB, DB, B and S5 213
8. Symmetric Gentzen Systems and Interpolation 214
9. Peculiar Non peculiarities of S5 221
10. An Embedding of S5 into S4 222
11. Another S5 Tableau System 225
12. Finite Axiomatizability 229
13. S5 Interpolation Theorems 234
14. The Significance of G 241
15. Tableau Rules for G 245
16. G Tableau Correctness 249
17. G Consistency Properties 251
18. Consequences 255
TABLE OF CONTENTS vii
CHAPTER SIX / NON NORMAL LOGICS
1. Introduction 262
2. Augmented Kripke Models 265
3. Semantic Tableaus 270
4. Consistency Properties 281
5. Deduction Theorems 286
6. Interpolation Theorems 292
7. Decidability 299
8. Axiom Systems 300
9. Natural Deduction Systems 306
10. Regular and Quasi regular Logics 313
11. Logics between Regular and Normal 316
12. The Intermediate Logics Axiomatized 321
13. The Logic U 329
CHAPTER SEVEN / QUANTIFIERS
1. Introduction 332
2. First order Languages 333
3. First order Models 339
4. Interpretations 343
5. Uniform Notation 344
6. Tableau Rules 345
7. Tableau Correctness 350
8. Analytic Consistency Properties 353
9. Analytic Tableau Completeness 366
10. Natural Deduction and Axiom Systems 367
11. Compactness and Skolem Lowenheim Theorems 372
12. Deduction Theorems 373
13. Interpolation Theorems 375
14. Dropping Monotonicity 380
15. Constant Domain Models 382
CHAPTER EIGHT / PREFIXED TABLEAU SYSTEMS
1. Introduction 386
2. Prefixed Propositional Tableaus 388
3. Correctness 398
4. A Systematic Tableau Procedure 401
5. Konig s Lemma 404
I
viii TABLE OF CONTENTS
6. Completeness 407
7. Decidability 410
8. Logical Consequence 416
9. The Fundamental Theorem 418
10. Quantifiers Constant Domains 424
11. Correctness and Completeness 425
12. Constant Domain Logics Axiomatically 428
13. Quantifiers Varying Domains 433
14. Concluding Remarks 436
CHAPTER NINE / INTUITIONISTIC LOGIC
1. Introduction 437
2. Propositional Intuitionistc Models 439
3. Independence of the Intuitionistic Connectives 444
4. Uniform Notation 450
5. Tableau Systems 453
6. Local and Global Satisfiability 462
7. Intuitionistic Consistency Properties 464
8. Decidability 468
9. First order Intuitionistic Models 469
10. Uniform Notation, again 474
11. First order Tableau Systems 476
12. First order Intuitionistic Consistency Properties 481
13. Consequences 485
14. An Axiom System 487
15. Axiomatic Correctness and Completeness 491
16. A Natural Deduction System 495
17. Direct Consequences 500
18. Completeness of the Natural Deduction System 504
19. Gentzen Systems and Interpolation 508
20. Concluding Comments 518
BIBLIOGRAPHY 526
INDEX 540
SPECIAL NOTATION 555
|
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| institution | BVB |
| isbn | 9027715734 |
| language | English |
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| physical | VIII, 555 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
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| publisher | Reidel |
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| series2 | Synthese library |
| spelling | Fitting, Melvin Verfasser aut Proof methods for modal and intuitionistic logics Melvin Fitting Dordrecht u.a. Reidel 1983 VIII, 555 S. txt rdacontent n rdamedia nc rdacarrier Synthese library 169 Intuitionistic mathematics Modality (Logic) Proof theory Intuitionistische Logik (DE-588)4162199-2 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Modallogik (DE-588)4074914-9 gnd rswk-swf Modallogik (DE-588)4074914-9 s Beweis (DE-588)4132532-1 s DE-604 Intuitionistische Logik (DE-588)4162199-2 s Synthese library 169 (DE-604)BV000005044 169 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000067969&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fitting, Melvin Proof methods for modal and intuitionistic logics Synthese library Intuitionistic mathematics Modality (Logic) Proof theory Intuitionistische Logik (DE-588)4162199-2 gnd Beweis (DE-588)4132532-1 gnd Modallogik (DE-588)4074914-9 gnd |
| subject_GND | (DE-588)4162199-2 (DE-588)4132532-1 (DE-588)4074914-9 |
| title | Proof methods for modal and intuitionistic logics |
| title_auth | Proof methods for modal and intuitionistic logics |
| title_exact_search | Proof methods for modal and intuitionistic logics |
| title_full | Proof methods for modal and intuitionistic logics Melvin Fitting |
| title_fullStr | Proof methods for modal and intuitionistic logics Melvin Fitting |
| title_full_unstemmed | Proof methods for modal and intuitionistic logics Melvin Fitting |
| title_short | Proof methods for modal and intuitionistic logics |
| title_sort | proof methods for modal and intuitionistic logics |
| topic | Intuitionistic mathematics Modality (Logic) Proof theory Intuitionistische Logik (DE-588)4162199-2 gnd Beweis (DE-588)4132532-1 gnd Modallogik (DE-588)4074914-9 gnd |
| topic_facet | Intuitionistic mathematics Modality (Logic) Proof theory Intuitionistische Logik Beweis Modallogik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000067969&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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