Mathematical logic for computer science:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London ; Heidelberg ; New York ; Dordrecht
Springer
2012
|
| Edition: | Third edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 346 Seiten Diagramme |
| ISBN: | 9781447141280 |
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| 245 | 1 | 0 | |a Mathematical logic for computer science |c Mordechai Ben-Ari |
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Record in the Search Index
| _version_ | 1804149370919059456 |
|---|---|
| adam_text | Titel: Mathematical logic for computer science
Autor: Ben-Arî, Môtî
Jahr: 2012
Contents
1 Introduction................................ 1
1.1 The Origins of Mathematical Logic................ 1
1.2 Propositional Logic........................ 2
1.3 First-Order Logic ......................... 3
1.4 Modal and Temporal Logics.................... 4
1.5 Program Verification........................ 5
1.6 Summary.............................. 5
1.7 Further Reading.......................... 6
1.8 Exercise.............................. 6
References................................. 6
2 Propositional Logic: Formulas, Models, Tableaux........... 7
2.1 Propositional Formulas...................... 7
2.2 Interpretations........................... 16
2.3 Logical Equivalence........................ 21
2.4 Sets of Boolean Operators *.................... 26
2.5 Satisfiability, Validity and Consequence.............. 29
2.6 Semantic Tableaux......................... 33
2.7 Soundness and Completeness................... 39
2.8 Summary.............................. 44
2.9 Further Reading.......................... 45
2.10 Exercises.............................. 45
References................................. 47
3 Propositional Logic: Deductive Systems ................ 49
3.1 Why Deductive Proofs?...................... 49
3.2 Gentzen System G......................... 51
3.3 Hilbert System H......................... 55
3.4 Derived Rules in H........................ 58
3.5 Theorems for Other Operators................... 62
3.6 Soundness and Completeness of H................ 64
3.7 Consistency ............................ 66
3.8 Strong Completeness and Compactness *............. 67
3.9 Variant Forms of the Deductive Systems * ............ 68
3.10 Summary.............................. 71
3.11 Further Reading.......................... 71
3.12 Exercises.............................. 72
References................................. 73
4 Propositional Logic: Resolution..................... 75
4.1 Conjunctive Normal Form..................... 75
4.2 Clausal Form............................ 77
4.3 Resolution Rule.......................... 80
4.4 Soundness and Completeness of Resolution * .......... 82
4.5 Hard Examples for Resolution *.................. 88
4.6 Summary.............................. 92
4.7 Further Reading.......................... 92
4.8 Exercises.............................. 92
References................................. 93
5 Propositional Logic: Binary Decision Diagrams............ 95
5.1 Motivation Through Truth Tables................. 95
5.2 Definition of Binary Decision Diagrams ............. 97
5.3 Reduced Binary Decision Diagrams................ 98
5.4 Ordered Binary Decision Diagrams................ 102
5.5 Applying Operators to BDDs................... 104
5.6 Restriction and Quantification *.................. 107
5.7 Summary.............................. 109
5.8 Further Reading.......................... 110
5.9 Exercises.............................. 110
References................................. 110
6 Propositional Logic: SAT Solvers.................... 111
6.1 Properties of Clausal Form .................... 111
6.2 Davis-Putnam Algorithm ..................... 115
6.3 DPLL Algorithm.......................... 116
6.4 An Extended Example of the DPLL Algorithm.......... 117
6.5 Improving the DPLL Algorithm.................. 122
6.6 Stochastic Algorithms....................... 125
6.7 Complexity of SAT * ....................... 126
6.8 Summary.............................. 128
6.9 Further Reading.......................... 128
6.10 Exercises.............................. 128
References................................. 129
7 First-Order Logic: Formulas, Models, Tableaux............ 131
7.1 Relations and Predicates...................... 131
7.2 Formulas in First-Order Logic................... 133
7.3 Interpretations........................... 136
7.4 Logical Equivalence........................ 140
7.5 Semantic Tableaux......................... 143
7.6 Soundness and Completion of Semantic Tableaux........ 150
7.7 Summary.............................. 153
7.8 Further Reading.......................... 153
7.9 Exercises.............................. 153
References................................. 154
8 First-Order Logic: Deductive Systems................. 155
8.1 Gentzen System G......................... 155
8.2 Hilbert System Jf......................... 158
8.3 Equivalence of H and G..................... 160
8.4 Proofs of Theorems in H..................... 161
8.5 TheC-Rule *............................ 163
8.6 Summary.............................. 165
8.7 Further Reading.......................... 165
8.8 Exercises.............................. 165
References................................. 166
9 First-Order Logic: Terms and Normal Forms............. 167
9.1 First-Order Logic with Functions................. 167
9.2 PCNF and Clausal Form...................... 172
9.3 Herbrand Models ......................... 177
9.4 Herbrand s Theorem *....................... 180
9.5 Summary.............................. 182
9.6 Further Reading.......................... 182
9.7 Exercises.............................. 182
References................................. 183
10 First-Order Logic: Resolution...................... 185
10.1 Ground Resolution......................... 185
10.2 Substitution ............................ 187
10.3 Unification............................. 189
10.4 General Resolution......................... 195
10.5 Soundness and Completeness of General Resolution *...... 198
10.6 Summary.............................. 202
10.7 Further Reading.......................... 202
10.8 Exercises.............................. 202
References................................. 203
11 First-Order Logic: Logic Programming................ 205
11.1 From Formulas in Logic to Logic Programming......... 205
11.2 Horn Clauses and SLD-Resolution ................ 209
11.3 Search Rules in SLD-Resolution ................. 213
11.4 Prolog............................... 216
11.5 Summary.............................. 220
11.6 Further Reading..........................221
11.7 Exercises..............................221
References.................................222
12 First-Order Logic: Undecidability and Model Theory * .......223
12.1 Undecidability of First-Order Logic................ 223
12.2 Decidable Cases of First-Order Logic............... 226
12.3 Finite and Infinite Models..................... 227
12.4 Complete and Incomplete Theories................ 228
12.5 Summary.............................. 229
12.6 Further Reading.......................... 229
12.7 Exercises.............................. 230
References................................. 230
13 Temporal Logic: Formulas, Models, Tableaux.............231
13.1 Introduction............................ 231
13.2 Syntax and Semantics....................... 233
13.3 Models of Time.......................... 237
13.4 Linear Temporal Logic ...................... 240
13.5 Semantic Tableaux......................... 244
13.6 Binary Temporal Operators *................... 258
13.7 Summary.............................. 260
13.8 Further Reading.......................... 261
13.9 Exercises.............................. 261
References................................. 262
14 Temporal Logic: A Deductive System..................263
14.1 Deductive System L .......................263
14.2 Theorems of L..........................264
14.3 Soundness and Completeness of L *...............269
14.4 Axioms for the Binary Temporal Operators *...........271
14.5 Summary..............................271
14.6 Further Reading..........................272
14.7 Exercises..............................272
References.................................272
15 Verification of Sequential Programs...................273
15.1 Correctness Formulas....................... 274
15.2 Deductive System H L...................... 275
15.3 Program Verification........................ 277
15.4 Program Synthesis......................... 279
15.5 Formal Semantics of Programs *................. 283
15.6 Soundness and Completeness of H L *............. 289
15.7 Summary.............................. 293
15.8 Further Reading.......................... 293
15.9 Exercises.............................. 293
References............... ... 295
16 Verification of Concurrent Programs.................. 297
16.1 Definition of Concurrent Programs................ 298
16.2 Formalization of Correctness ................... 300
16.3 Deductive Verification of Concurrent Programs.......... 303
16.4 Programs as Automata....................... 307
16.5 Model Checking of Invariance Properties............. 311
16.6 Model Checking of Liveness Properties.............. 314
16.7 Expressing an LTL Formula as an Automaton .......... 315
16.8 Model Checking Using the Synchronous Automaton....... 317
16.9 Branching-Time Temporal Logic *................ 319
16.10 Symbolic Model Checking * ................... 322
16.11 Summary.............................. 323
16.12 Further Reading.......................... 324
16.13 Exercises.............................. 324
References................................. 325
Appendix Set Theory............................ 327
A.l Finite and Infinite Sets....................... 327
A.2 Set Operators............................ 328
A.3 Sequences............................. 330
A.4 Relations and Functions...................... 331
A.5 Cardinality............................. 333
A.6 Proving Properties of Sets..................... 335
References................................. 336
Index of Symbols................................ 337
Name Index................................... 339
Subject Index.................................. 341
|
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| discipline | Informatik Mathematik |
| edition | Third edition |
| format | Book |
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| spelling | Ben-Arî, Môtî 1948- (DE-588)121144844 aut Mathematical logic for computer science Mordechai Ben-Ari Third edition London ; Heidelberg ; New York ; Dordrecht Springer 2012 xv, 346 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Logische Programmierung (DE-588)4195096-3 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 Logik (DE-588)4036202-4 s Informatik (DE-588)4026894-9 s 1\p DE-604 Logische Programmierung (DE-588)4195096-3 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4471-4129-7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025192957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ben-Arî, Môtî 1948- Mathematical logic for computer science Mathematische Logik (DE-588)4037951-6 gnd Logische Programmierung (DE-588)4195096-3 gnd Informatik (DE-588)4026894-9 gnd Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4195096-3 (DE-588)4026894-9 (DE-588)4036202-4 (DE-588)4123623-3 |
| title | Mathematical logic for computer science |
| title_auth | Mathematical logic for computer science |
| title_exact_search | Mathematical logic for computer science |
| title_full | Mathematical logic for computer science Mordechai Ben-Ari |
| title_fullStr | Mathematical logic for computer science Mordechai Ben-Ari |
| title_full_unstemmed | Mathematical logic for computer science Mordechai Ben-Ari |
| title_short | Mathematical logic for computer science |
| title_sort | mathematical logic for computer science |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Logische Programmierung (DE-588)4195096-3 gnd Informatik (DE-588)4026894-9 gnd Logik (DE-588)4036202-4 gnd |
| topic_facet | Mathematische Logik Logische Programmierung Informatik Logik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025192957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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