Completeness theory for propositional logics:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston, Mass. ; Berlin
Birkhäuser
2008
|
| Series: | Studies in universal logic
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 165 - 174 |
| Physical Description: | VIII, 178 S. 24 cm |
| ISBN: | 9783764385170 3764385170 |
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| 245 | 1 | 0 | |a Completeness theory for propositional logics |c Witold A. Pogorzelski ; Piotr Wojtylak |
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Record in the Search Index
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| adam_text | Contents
Introduction vii
1 Basic notions 1
1.1 Propositional languages........................ 1
1.2 Abstract algebras............................ 3
1.3 Preliminary lattice-theoretical notions................ 6
1.4 Propositional logics........................... 19
1.5 Brief exposition of the most important propositional logics..... 31
2 Semantic methods in propositional logic 41
2.1 Preordered sets............................. 41
2.2 Preordered algebras .......................... 50
2.3 Logical matrices ............................ 55
2.4 Adequacy................................ 63
2.5 Propositional logic and lattice theory................. 75
3 Completeness of propositional logics 91
3.1 Generalized completeness....................... 91
3.2 Post-completeness ........................... 97
3.3 The problem of uniqueness of Lindenbaum extensions ....... 105
3.4 Structural completeness........................ 112
3.5 Some related concepts......................... 120
4 Characterizations of propositional connectives 131
4.1 Cn-definitions.............................. 131
4.2 The system (D)............................. 133
4.3 Variants................................. 137
4.4 The system (I) ............................. 141
4.5 Classical logic.............................. 149
Appendix A
The fundamental metatheorem for the classical propositional logic 153
vi Contents
Appendix B
A proof system for the classical logic 157
Bibliography 165
Notation 175
Index 177
|
| adam_txt |
Contents
Introduction vii
1 Basic notions 1
1.1 Propositional languages. 1
1.2 Abstract algebras. 3
1.3 Preliminary lattice-theoretical notions. 6
1.4 Propositional logics. 19
1.5 Brief exposition of the most important propositional logics. 31
2 Semantic methods in propositional logic 41
2.1 Preordered sets. 41
2.2 Preordered algebras . 50
2.3 Logical matrices . 55
2.4 Adequacy. 63
2.5 Propositional logic and lattice theory. 75
3 Completeness of propositional logics 91
3.1 Generalized completeness. 91
3.2 Post-completeness . 97
3.3 The problem of uniqueness of Lindenbaum extensions . 105
3.4 Structural completeness. 112
3.5 Some related concepts. 120
4 Characterizations of propositional connectives 131
4.1 Cn-definitions. 131
4.2 The system (D). 133
4.3 Variants. 137
4.4 The system (I) . 141
4.5 Classical logic. 149
Appendix A
The fundamental metatheorem for the classical propositional logic 153
vi Contents
Appendix B
A proof system for the classical logic 157
Bibliography 165
Notation 175
Index 177 |
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| spelling | Pogorzelski, Witold A. Verfasser aut Completeness theory for propositional logics Witold A. Pogorzelski ; Piotr Wojtylak Basel ; Boston, Mass. ; Berlin Birkhäuser 2008 VIII, 178 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Studies in universal logic Literaturverz. S. 165 - 174 Completeness theorem Aussagenlogik (DE-588)4136098-9 gnd rswk-swf Vollständigkeit (DE-588)4284513-0 gnd rswk-swf Aussagenlogik (DE-588)4136098-9 s Vollständigkeit (DE-588)4284513-0 s DE-604 Wojtylak, Piotr Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016584987&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pogorzelski, Witold A. Wojtylak, Piotr Completeness theory for propositional logics Completeness theorem Aussagenlogik (DE-588)4136098-9 gnd Vollständigkeit (DE-588)4284513-0 gnd |
| subject_GND | (DE-588)4136098-9 (DE-588)4284513-0 |
| title | Completeness theory for propositional logics |
| title_auth | Completeness theory for propositional logics |
| title_exact_search | Completeness theory for propositional logics |
| title_exact_search_txtP | Completeness theory for propositional logics |
| title_full | Completeness theory for propositional logics Witold A. Pogorzelski ; Piotr Wojtylak |
| title_fullStr | Completeness theory for propositional logics Witold A. Pogorzelski ; Piotr Wojtylak |
| title_full_unstemmed | Completeness theory for propositional logics Witold A. Pogorzelski ; Piotr Wojtylak |
| title_short | Completeness theory for propositional logics |
| title_sort | completeness theory for propositional logics |
| topic | Completeness theorem Aussagenlogik (DE-588)4136098-9 gnd Vollständigkeit (DE-588)4284513-0 gnd |
| topic_facet | Completeness theorem Aussagenlogik Vollständigkeit |
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