A study of logics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Clarendon Press
1991
|
| Series: | Oxford logic guides
18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 417 S. graph. Darst. |
| ISBN: | 0198532113 |
Staff View
MARC
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| 245 | 1 | 0 | |a A study of logics |c John P. Cleave |
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Record in the Search Index
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| adam_text | Contents
Glossary of notation xi
1. The multiplicity of logics 1
1.1 The province of logic 1
1.2 The development of the concept of deductive science 5
1.3 Criticisms of the positivist view 8
1.4 The science of logics 12
1.5 Logics 14
2. Classical logic 16
2.1 Introduction 16
2.2 Propositional logic 19
2.3 Predicate logic 38
3. Abstract logics 58
3.1 Introduction 58
3.2 Prelogics 59
3.3 Conditions on prelogics 65
3.4 Transfer principles 69
3.5 Logics 75
3.6 Closed sets 79
3.7 Logical operations 82
3.8 Compact logics 89
3.9 Formal systems and combinatorial systems 93
3.10 Finite logics 96
3.11 Gentzen systems 98
3.12 Comparison of logics 102
4. Logical operations 105
4.1 Connectives 105
4.2 The historical connectives 106
4.3 Relations between connectives 125
4.4 Quantifiers 129
4.5 Quantifiers and connectives 132
viii Contents
5. Order and lattices 136
5.1 Introduction 136
5.2 Relations 136
5.3 Equivalence relations 140
5.4 Abstraction 142
5.5 Order 145
5.6 Upper and lower bounds 151
5.7 Lattices 155
5.8 Complete lattices 161 !
5.9 Various kinds of lattices 163
5.10 Complemented lattices 175
6. Constructing logics 193
6.1 Introduction 193
6.2 Many valued logics 193
6.3 Logics from truth values 195
6.4 Logics from lattices 199
6.5 Logical consequence in classical logic 202
6.6 Logical consequence in semantic logics 204
6.7 Functionally free algebras 208
6.8 The logic of quantum mechanics 209
6.9 Predicate logics 212
6.10 Temporal logics 218
6.11 Model structures 225
7. Quasi Boolean algebras and empirical continuity 228
7.1 Introduction 228
7.2 Quasi Boolean algebras 228
7.3 Constructing quasi Boolean algebras 230
7.4 The boundary elements of a quasi Boolean algebra 233
7.5 Quasi Boolean algebras in relation to Boolean algebras 235
7.6 The structure of quasi Boolean algebras 238
7.7 Inexact classes and predicates 243
7.8 Empirical continuity 247
8. Three valued logic 253
8.1 Introduction 253
8.2 The classical imperative 253
8.3 Sources of the third truth value 255
8.4 The logics of truth values 257
8.5 The continuity principle for truth values 258
Contents ix
8.6 N3 propositional calculus 263
8.7 Normal forms and the analysis of implications 268
8.8 The nucleus of fi[N3]lf 272
8.9 Connectivity and continuity in £[N3]]} 274
8.10 Three valued predicate calculus 275
9. Relevance 286
9.1 Introduction 286
9.2 Rigid propositions 288
9.3 Minimal implications 298
9.4 A semantic method 305
10. The calculus of logics: effective logic 309
10.1 Introduction 309
10.2 Effective extension of a logic 312
10.3 The cut condition 316
10.4 The triviality condition 324
10.5 Regular junctors and effective positive logic 326
10.6 Negation in effective logic 328
10.7 Effective quantifier logics 330
10.8 Effective, intuitionistic, and classical logics 339
10.9 Brouwer s intuitionism 341
10.10 Bishop s constructivism 353
10.11 Other kinds of constructivism 356
11. Modal logics 360
11.1 Introduction 360
11.2 Necessity and logic 363
11.3 Relative necessity 365
11.4 Constructing a classical modal logic 367
11.5 Axiomatizability of theories of necessity 372
11.6 Axiomatization of the general theory of necessity 374
11.7 Effective modal logics 377
11.8 Deontic logic 385
Appendix 390
References 397
Index 411
|
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| isbn | 0198532113 |
| language | English |
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| physical | XIII, 417 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Clarendon Press |
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| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Cleave, John P. Verfasser aut A study of logics John P. Cleave Oxford [u.a.] Clarendon Press 1991 XIII, 417 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 18 Formele logica gtt Logique symbolique et mathématique ram Wiskundige logica gtt Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Logik (DE-588)4036202-4 s Oxford logic guides 18 (DE-604)BV000013997 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003888436&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cleave, John P. A study of logics Oxford logic guides Formele logica gtt Logique symbolique et mathématique ram Wiskundige logica gtt Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4037951-6 |
| title | A study of logics |
| title_auth | A study of logics |
| title_exact_search | A study of logics |
| title_full | A study of logics John P. Cleave |
| title_fullStr | A study of logics John P. Cleave |
| title_full_unstemmed | A study of logics John P. Cleave |
| title_short | A study of logics |
| title_sort | a study of logics |
| topic | Formele logica gtt Logique symbolique et mathématique ram Wiskundige logica gtt Logic, Symbolic and mathematical Logik (DE-588)4036202-4 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Formele logica Logique symbolique et mathématique Wiskundige logica Logic, Symbolic and mathematical Logik Mathematische Logik |
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