Proof theory and automated deduction:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1997
|
| Schriftenreihe: | Applied logic series
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 424 S. graph. Darst. |
| ISBN: | 0792345932 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011602376 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 971031s1997 d||| |||| 00||| eng d | ||
| 020 | |a 0792345932 |9 0-7923-4593-2 | ||
| 035 | |a (OCoLC)36841601 | ||
| 035 | |a (DE-599)BVBBV011602376 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 | ||
| 050 | 0 | |a QA9.54 | |
| 082 | 0 | |a 511.3 |2 21 | |
| 084 | |a SK 130 |0 (DE-625)143216: |2 rvk | ||
| 100 | 1 | |a Goubault-Larrecq, Jean |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Proof theory and automated deduction |c by Jean Goubault-Larrecq and Ian Mackie |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1997 | |
| 300 | |a XV, 424 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied logic series |v 6 | |
| 650 | 4 | |a Automatic theorem proving | |
| 650 | 4 | |a Proof theory | |
| 700 | 1 | |a Mackie, Ian |e Verfasser |4 aut | |
| 830 | 0 | |a Applied logic series |v 6 |w (DE-604)BV011076498 |9 6 | |
| 856 | 4 | 2 | |m SWB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007815849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007815849 | ||
Datensatz im Suchindex
| _version_ | 1804126131830390784 |
|---|---|
| adam_text | CONTENTS LIST OF FIGURES XI PREFACE XIII ACKNOWLEDGEMENTS XV CHAPTER 1
INTRODUCTION 1 1 OVERVIEW 6 CHAPTER 2 CLASSICAL PROPOSITIONAL LOGIC 11 1
SYNTAX 11 2 SEMANTICS 15 3 DEDUCTION SYSTEMS 19 3.1 HILBERT-STYLE
SYSTEMS 20 3.2 NATURAL DEDUCTION 24 3.3 GENTZEN SEQUENTS 36 4 AUTOMATED
PROOF METHODS 40 4.1 TABLEAUX 40 4.2 PREPOSITIONAL RESOLUTION 47 4.3 THE
DAVIS-PUTNAM METHOD 53 4.4 BINARY DECISION DIAGRAMS 56 5 DIGRESSIONS 66
5.1 EXPRESSIVENESS OF PREPOSITIONAL CLASSICAL LOGIC 66 5.2 BOOLEAN
ALGEBRAS 68 5.3 QUANTIFIED PREPOSITIONAL LOGIC 71 CHAPTER 3 OTHER
PROPOSITIONAL LOGICS 73 1 INTRODUCTION 73 1.1 CONSTRUCTIVITY 73 1.2
RESOURCES 75 1.3 SEMANTIC PARADIGMS 76 1.4 NOTATION 77 2 INTUITIONISTIC
LOGIC 79 2.1 INTUITIONISTIC NATURAL DEDUCTION (NJ 0 ) 80 2.2
INTUITIONISTIC SEQUENT CALCULUS (LJ 0 ) 83 VIII PROOF THEORY AND
AUTOMATED DEDUCTION 2.3 RELATING SEQUENT CALCULUS AND NATURAL DEDUCTION
85 2.4 HILBERT-STYLE PRESENTATION 89 3 NORMALISATION AND CUT ELIMINATION
95 3.1 NORMALISATION 96 3.2 CUT ELIMINATION 98 4 SEMANTICS OF
INTUITIONISTIC LOGIC 102 4.1 KRIPKE SEMANTICS 102 4.2 INTUITIONISTIC
TABLEAUX 106 4.3 FUNCTIONAL INTERPRETATION 110 5 RELATING INTUITIONISTIC
AND CLASSICAL LOGIC ILL 6 ADDITIVE AND MULTIPLICATIVE CONNECTIVES 117 7
LINEAR LOGIC 119 7.1 SYNTAX OF LINEAR LOGIC 120 7.2 CLASSICAL LINEAR
SEQUENT CALCULUS 121 7.3 CODING INTUITIONISTIC LOGIC 126 CHAPTER 4 THE
CURRY-HOWARD CORRESPONDENCE 131 1 INTRODUCTION 131 1.1 FUNCTIONS 133 2
TYPED A-CALCULUS AND NATURAL DEDUCTION 134 2.1 TYPED A-CALCULUS 134 2.2
TERM ASSIGNMENT FOR NATURAL DEDUCTION 139 2.3 PROPERTIES 143 3
COMBINATORY LOGIC AND HILBERT-STYLE AXIOMS . . . . 147 3.1 COMBINATORY
LOGIC 147 3.2 THE CORRESPONDENCE WITH HILBERT AXIOMS 150 4 APPLICATIONS
OF THE CURRY-HOWARD CORRESPONDENCE 152 4.1 SYSTEM F 153 CHAPTER 5 MODAL
AND TEMPORAL LOGICS 157 1 INTRODUCTION AND MOTIVATION 157 2 S4 AND
NON-MONOTONIC LOGICS 158 2.1 SYNTAX 158 2.2 PHILOSOPHICAL LOGIC AND
NON-MONOTONIC LOGICS 159 2.3 KRIPKE SEMANTICS 161 2.4 DECIDABILITY 165
2.5 SEQUENT SYSTEMS AND TABLEAUX 168 3 OTHER MODAL LOGICS OF INTEREST IN
COMPUTER SCIENCE 170 3.1 HENNESSY-MILNER LOGIC 170 3.2 CTL 172 3.3
PROPOSITIONAL DYNAMIC LOGIC 173 4 MODEL-CHECKING 176 4.1 SEQUENTIAL
MACHINES AND SYMBOLIC MODEL-CHECKING 177 EDITORIAL PREFACE IX 4.2 BINARY
DECISION DIAGRAMS 181 4.3 DEVELOPMENTS 182 CHAPTER 6 FIRST-ORDER
CLASSICAL LOGIC 185 1 DEFINITIONS 185 1.1 SYNTAX 185 2 SEMANTICS 188 3
DEDUCTION SYSTEMS 190 4 EXPRESSIVE POWER 191 5 META-MATHEMATICAL
PROPERTIES 197 5.1 PRENEX AND SKOLEM FORMS 197 5.2 SEMANTIC HERBRAND
THEORY 201 5.3 CUT-ELIMINATION AND SYNTACTIC HERBRAND THEORY 210 6
DIGRESSIONS 220 6.1 NON-CLASSICAL LOGICS 221 6.2 ARITHMETIC 221 6.3
HIGHER-ORDER LOGICS 224 CHAPTER 7 RESOLUTION 233 1 FUNDAMENTAL IDEAS 233
2 UNIFICATION 235 3 RESOLUTION 241 4 OPTIMISATIONS 244 4.1 CLAUSE
SELECTION STRATEGIES 244 4.2 DELETION STRATEGIES 245 4.3 ORDERING
STRATEGIES 250 4.4 SEMANTIC RESOLUTION AND SET-OF-SUPPORT STRATEGIES 254
4.5 THE LINEAR STRATEGY 260 4.6 OTHER REFINEMENTS OF RESOLUTION 263 5
RESOLUTION AS CUT-ONLY PROOFS 264 CHAPTER 8 TABLEAUX, CONNECTIONS AND
MATINGS 269 1 FIRST-ORDER TABLEAUX 269 1.1 USING HERBRAND S THEOREM 270
1.2 EXTENSION STEPS 273 2 FREE VARIABLE TABLEAUX 274 2.1 PRESENTATION
274 2.2 HERBRANDIZING ON-THE-FLY 276 2.3 DISCUSSION 279 3 CONNECTIONS,
MATINGS AND MODEL ELIMINATION . . . .281 3.1 CONNECTIONS AND MATINGS 281
3.2 RELATION WITH RESOLUTION 282 3.3 CHANG S V-RESOLUTION 285 X PROOF
THEORY AND AUTOMATED DEDUCTION 3.4 MODEL ELIMINATION 287 CHAPTER 9
INCORPORATING KNOWLEDGE 293 1 MOTIVATIONS 293 2 EQUALITY AND REWRITING
295 2.1 REWRITING 295 2.2 PARAMODULATION, OR INTEGRATING REWRITING WITH
RESOLUTION 306 2.3 EQUALITY AND TABLEAUX 310 2.4 RIGID E-UNIFICATION 312
3 EQUATIONAL THEORIES 317 3.1 HERBRAND THEORY MODULO AN EQUATIONAL
THEORY 318 3.2 E-UNIFICATION 319 3.3 PARTICULAR THEORIES 323 3.4 FURTHER
READING 325 4 OTHER THEORIES 325 4.1 SORTS 325 4.2 THEORY RESOLUTION 331
4.3 GROBNER BASES 333 CHAPTER 10 LOGIC PROGRAMMING LANGUAGES 341 1
INTRODUCTION 341 2 PROLOG 343 3 CONSTRAINTS 350 4 PARALLELISM 354 4.1
OR-PARALLELISM 354 4.2 AND-PARALLELISM 356 APPENDIX A ANSWERS TO
EXERCISES 357 APPENDIX B BASICS OF TOPOLOGY 403 BIBLIOGRAPHY 407 INDEX
415
|
| any_adam_object | 1 |
| author | Goubault-Larrecq, Jean Mackie, Ian |
| author_facet | Goubault-Larrecq, Jean Mackie, Ian |
| author_role | aut aut |
| author_sort | Goubault-Larrecq, Jean |
| author_variant | j g l jgl i m im |
| building | Verbundindex |
| bvnumber | BV011602376 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.54 |
| callnumber-search | QA9.54 |
| callnumber-sort | QA 19.54 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 |
| ctrlnum | (OCoLC)36841601 (DE-599)BVBBV011602376 |
| 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 | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01297nam a2200361 cb4500</leader><controlfield tag="001">BV011602376</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">971031s1997 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792345932</subfield><subfield code="9">0-7923-4593-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)36841601</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011602376</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA9.54</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 130</subfield><subfield code="0">(DE-625)143216:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Goubault-Larrecq, Jean</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Proof theory and automated deduction</subfield><subfield code="c">by Jean Goubault-Larrecq and Ian Mackie</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht [u.a.]</subfield><subfield code="b">Kluwer</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 424 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Applied logic series</subfield><subfield code="v">6</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Automatic theorem proving</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proof theory</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mackie, Ian</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applied logic series</subfield><subfield code="v">6</subfield><subfield code="w">(DE-604)BV011076498</subfield><subfield code="9">6</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">SWB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007815849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007815849</subfield></datafield></record></collection> |
| id | DE-604.BV011602376 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:12:35Z |
| institution | BVB |
| isbn | 0792345932 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007815849 |
| oclc_num | 36841601 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | XV, 424 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
| record_format | marc |
| series | Applied logic series |
| series2 | Applied logic series |
| spelling | Goubault-Larrecq, Jean Verfasser aut Proof theory and automated deduction by Jean Goubault-Larrecq and Ian Mackie Dordrecht [u.a.] Kluwer 1997 XV, 424 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied logic series 6 Automatic theorem proving Proof theory Mackie, Ian Verfasser aut Applied logic series 6 (DE-604)BV011076498 6 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007815849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goubault-Larrecq, Jean Mackie, Ian Proof theory and automated deduction Applied logic series Automatic theorem proving Proof theory |
| title | Proof theory and automated deduction |
| title_auth | Proof theory and automated deduction |
| title_exact_search | Proof theory and automated deduction |
| title_full | Proof theory and automated deduction by Jean Goubault-Larrecq and Ian Mackie |
| title_fullStr | Proof theory and automated deduction by Jean Goubault-Larrecq and Ian Mackie |
| title_full_unstemmed | Proof theory and automated deduction by Jean Goubault-Larrecq and Ian Mackie |
| title_short | Proof theory and automated deduction |
| title_sort | proof theory and automated deduction |
| topic | Automatic theorem proving Proof theory |
| topic_facet | Automatic theorem proving Proof theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007815849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011076498 |
| work_keys_str_mv | AT goubaultlarrecqjean prooftheoryandautomateddeduction AT mackieian prooftheoryandautomateddeduction |