First order logic and automated theorem proving:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1996
|
| Edition: | 2. ed. |
| Series: | Graduate texts in computer science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | WST: First-order logic and automated theorem proving. - Literaturverz. S. 315 - 318 |
| Physical Description: | XVI, 326 S. |
| ISBN: | 0387945938 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text |
MELVIN FITTING
FIRST-ORDER LOGIC
AND
AUTOMATED
THEOREM
PROVING
SECOND EDITION
SPRINGER
CONTENTS
PREFACE VII
PREFACE TO THE SECOND EDITION XI
1 BACKGROUND 1
2 PROPOSITIONAL LOGIC 9
2.1 INTRODUCTION 9
2.2 PROPOSITIONAL LOGIC-SYNTAX 10
2.3 PROPOSITIONAL LOGIC-SEMANTICS 14
2.4 BOOLEAN VALUATIONS 16
2.5 THE REPLACEMENT THEOREM 20
2.6 UNIFORM NOTATION 23
2.7 KONIG'S LEMMA 26
2.8 NORMAL FORMS 27
2.9 NORMAL FORM IMPLEMENTATIONS 35
XIV CONTENTS
3 SEMANTIC TABLEAUX AND RESOLUTION 41
3.1 PROPOSITIONAL SEMANTIC TABLEAUX 41
3.2 PROPOSITIONAL TABLEAUX IMPLEMENTATIONS 47
3.3 PROPOSITIONAL RESOLUTION ., 51
3.4 SOUNDNESS 55
3.5 HINTIKKA'S LEMMA 58
3.6 THE MODEL EXISTENCE THEOREM 59
3.7 TABLEAU AND RESOLUTION COMPLETENESS 64
3.8 COMPLETENESS WITH RESTRICTIONS 69
3.9 PROPOSITIONAL CONSEQUENCE 74
4 OTHER PROPOSITIONAL PROOF PROCEDURES 77
4.1 HILBERT SYSTEMS 77
4.2 NATURAL DEDUCTION 86
4.3 THE SEQUENT CALCULUS 92
4.4 THE DAVIS-PUTNAM PROCEDURE 98
4.5 COMPUTATIONAL COMPLEXITY 104
5 FIRST-ORDER LOGIC 109.
5.1 FIRST-ORDER LOGIC-SYNTAX 109
5.2 SUBSTITUTIONS 113
5.3 FIRST-ORDER SEMANTICS 117
5.4 HERBRAND MODELS 123
5.5 FIRST-ORDER UNIFORM NOTATION 124
5.6 HINTIKKA'S LEMMA 127
5.7 PARAMETERS 128
5.8 THE MODEL EXISTENCE THEOREM 129
5.9 APPLICATIONS 132
5.10 LOGICAL CONSEQUENCE . . 135
CONTENTS XV
6 FIRST-ORDER PROOF
PROCEDURES
137
6.1
FIRST-ORDER SEMANTIC TABLEAUX 137
6.2 FIRST-ORDER RESOLUTION 141
6.3 SOUNDNESS 142
6.4 COMPLETENESS 143
6.5 HILBERT SYSTEMS 146
6.6 NATURAL DEDUCTION AND GENTZEN SEQUENTS 149
7 IMPLEMENTING TABLEAUX AND RESOLUTION 151
7.1 WHAT NEXT 151
7.2 UNIFICATION 152
7.3 UNIFICATION IMPLEMENTED 161
7.4 FREE-VARIABLE SEMANTIC TABLEAUX 166
7.5 A TABLEAU IMPLEMENTATION 169
7.6 FREE-VARIABLE RESOLUTION 184
7.7 SOUNDNESS 188
7.8 FREE-VARIABLE TABLEAU COMPLETENESS 191
7.9 FREE-VARIABLE RESOLUTION COMPLETENESS 196
8 FURTHER FIRST-ORDER FEATURES 203
8.1 INTRODUCTION 203
8.2 THE REPLACEMENT THEOREM 203
8.3 SKOLEMIZATION 206
8.4 PRENEX FORM 209
8.5 THE AE-CALCULUS 212
8.6 HERBRAND'S THEOREM 215
8.7 HERBRAND'S THEOREM, CONSTRUCTIVELY 221
8.8 GENTZEN'S THEOREM 225
8.9 CUT ELIMINATION 228
8.10 DO CUTS SHORTEN PROOFS? 243
8.11 CRAIG'S INTERPOLATION THEOREM 254
8.12 CRAIG'S INTERPOLATION THEOREM-CONSTRUCTIVELY 257
8.13 BETH'S DEFINABILITY THEOREM 263
8.14 LYNDON'S HOMORNORPHISM THEOREM 266
XVI CONTENTS
9 EQUALITY
271
9.1 INTRODUCTION 271
9.2 SYNTAX AND SEMANTICS 273
9.3 THE EQUALITY AXIOMS 276
9.4 HINTIKKA'S LEMMA 279
9.5 THE MODEL EXISTENCE THEOREM 284
9.6 CONSEQUENCES 285
9.7 TABLEAU AND RESOLUTION SYSTEMS 288
9.8 ALTERNATE TABLEAU AND RESOLUTION SYSTEMS 294
9.9 A FREE-VARIABLE TABLEAU SYSTEM WITH EQUALITY 298
9.10 A TABLEAU IMPLEMENTATION WITH EQUALITY 305
9.11 PARAMODULATION 312
REFERENCES .
315
INDEX 319 |
| any_adam_object | 1 |
| author | Fitting, Melvin |
| author_facet | Fitting, Melvin |
| author_role | aut |
| author_sort | Fitting, Melvin |
| author_variant | m f mf |
| building | Verbundindex |
| bvnumber | BV010613253 |
| classification_rvk | SK 130 ST 304 |
| classification_tum | MAT 030f DAT 706f DAT 540f |
| ctrlnum | (OCoLC)247119105 (DE-599)BVBBV010613253 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2025-03-10T13:02:59Z |
| institution | BVB |
| isbn | 0387945938 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007080864 |
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| physical | XVI, 326 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series2 | Graduate texts in computer science |
| spelling | Fitting, Melvin Verfasser aut First order logic and automated theorem proving Melvin Fitting First-order logic and automated theorem proving 2. ed. New York [u.a.] Springer 1996 XVI, 326 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in computer science WST: First-order logic and automated theorem proving. - Literaturverz. S. 315 - 318 Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf Stufe 1 (DE-588)4362503-4 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 s Stufe 1 (DE-588)4362503-4 s Automatisches Beweisverfahren (DE-588)4069034-9 s DE-604 Mathematische Logik (DE-588)4037951-6 s 1\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007080864&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fitting, Melvin First order logic and automated theorem proving Mathematische Logik (DE-588)4037951-6 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Stufe 1 (DE-588)4362503-4 gnd Prädikatenlogik (DE-588)4046974-8 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4069034-9 (DE-588)4362503-4 (DE-588)4046974-8 |
| title | First order logic and automated theorem proving |
| title_alt | First-order logic and automated theorem proving |
| title_auth | First order logic and automated theorem proving |
| title_exact_search | First order logic and automated theorem proving |
| title_full | First order logic and automated theorem proving Melvin Fitting |
| title_fullStr | First order logic and automated theorem proving Melvin Fitting |
| title_full_unstemmed | First order logic and automated theorem proving Melvin Fitting |
| title_short | First order logic and automated theorem proving |
| title_sort | first order logic and automated theorem proving |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Stufe 1 (DE-588)4362503-4 gnd Prädikatenlogik (DE-588)4046974-8 gnd |
| topic_facet | Mathematische Logik Automatisches Beweisverfahren Stufe 1 Prädikatenlogik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007080864&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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