Automated development of fundamental mathematical theories:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1992
|
| Schriftenreihe: | Automated reasoning series
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 271 S. |
| ISBN: | 0792320212 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV008048236 | ||
| 003 | DE-604 | ||
| 005 | 20100805 | ||
| 007 | t | ||
| 008 | 930720s1992 |||| 00||| eng d | ||
| 020 | |a 0792320212 |9 0-7923-2021-2 | ||
| 035 | |a (OCoLC)26722530 | ||
| 035 | |a (DE-599)BVBBV008048236 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-29T |a DE-91G |a DE-19 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA76.9.A96 | |
| 082 | 0 | |a 511.3 |2 20 | |
| 084 | |a SK 130 |0 (DE-625)143216: |2 rvk | ||
| 084 | |a DAT 706f |2 stub | ||
| 100 | 1 | |a Quaife, Art |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Automated development of fundamental mathematical theories |c by Art Quaife |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1992 | |
| 300 | |a XVIII, 271 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Automated reasoning series |v 2 | |
| 650 | 4 | |a Künstliche Intelligenz | |
| 650 | 4 | |a Artificial intelligence | |
| 650 | 4 | |a Automatic theorem proving | |
| 650 | 0 | 7 | |a Automatisches Beweisverfahren |0 (DE-588)4069034-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Automatisches Beweisverfahren |0 (DE-588)4069034-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Automatisches Beweisverfahren |0 (DE-588)4069034-9 |D s |
| 689 | 1 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 1 | |5 DE-188 | |
| 830 | 0 | |a Automated reasoning series |v 2 |w (DE-604)BV004807212 |9 2 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005295687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005295687 | ||
Datensatz im Suchindex
| _version_ | 1804122413309362176 |
|---|---|
| adam_text | Contents
Preface. A Personal View of Automated Reasoning Research xi
Chapter 1. Introduction to Automated Reasoning
1. Introduction 1
2. The potential scope of automated reasoning 1
3. The current scope of automated reasoning 3
4. Mathematical logic 4
5. Automation of first order logic 4
6. Clauses 5
7. Conversion to clausal form 7
8. Cut rule 8
9. Substitutions 8
10. Unification algorithm 10
11. Binary resolution 11
12. Binary resolution is dead, long live binary resolution! 12
13. Hyperresolution 13
14. UR resolution 13
15. Equality reasoning 14
16. Other strategies for fighting the combinatorial explosion 17
17. Infinite schemata 18
18. Theorem provers used in this work 19
19. Outline of remaining chapters 20
20. Survey of principal literature 22
Chapter 2. Von Neumann Bernays Godel Set Theory
1. Introduction 23
2. Notation 25
3. Simplifications 26
3.1. Sethood 26
3.2. Equality 27
3.3. Introduction of ordered pairs 27
3.4. Use of ordered pairs 28
3.5. Constructor axioms 29
3.6. Class existence theorem 30
3.7. Constructors versus Skolem functors 32
viii CONTENTS
4. Clauses for axioms and definitions 34
5. Proving classes equal 42
6. Boolean demodulators 46
7. Skolem functors and the Axiom of Choice 49
8. Theorems proved 50
9. Use of previously proved theorems 50
10. Heuristics and option settings 51
11. Proof finder or proof verifier? 53
12. Proof of Cantor s theorem 54
13. Proof that the composition of homomorphisms
is a homomorphism 56
14. Developing a unification algorithm
appropriate to NBG set theory 63
15. Conclusion 64
Chapter 3. Peano s Arithmetic
1. Introduction 65
2. The axioms 67
3. Theorems proved 68
4. Numerals 69
5. Difference 70
6. Ordering relation 70
7. Induction 71
8. Connection with NBG set theory 73
9. Introduction of new functors 74
10. Definition by primitive recursion 75
11. Definition of lists 75
12. A schema for proving metatheorems 77
13. Greek classics 1:
The square root of any prime is irrational 80
14. Greek classics 2: There are infinitely many primes 82
15. Unique factorization 84
16. Prime power factorization of greatest common divisor 86
17. Euler s theorem 88
18. Related research 89
19. Goldbach s conjecture 90
CONTENTS ix
Chapter 4. Tarski s Geometry
1. Introduction 92
2. The axioms 93
3. Comparison with earlier system 96
4. Automated proof procedures 97
5. Canonicalization in absence of commutative unification 98
6. Theorems proved 99
7. Proofs of challenge theorems 106
8. Performance statistics 116
9. Related research 117
10. Further challenges 117
11. Discussion 118
Chapter 5. Lob s Theorem and
Godel s Two Incompleteness Theorems
1. Introduction 120
2. Background and motivation 120
3. Theorems of Godel and Lob 122
4. The modal logic calculus K4 123
5. Formalization of K4 within OTTER 125
5.1. Tautologies 126
5.2. Comments on demodulators 129
6. Intermediate results 131
7. Lob s theorem 132
8. Godel s first incompleteness theorem 134
9. Godel s second incompleteness theorem 135
10. Further research 136
11. Conclusion 137
Chapter 6. Unsolved Problems in Elementary Number Theory
1. Introduction 138
2. The problems 139
3. Conclusion and beginning 150
x CONTENTS
Appendix 1. Godel s Axioms for Set Theory 151
Appendix 2. Theorems Proved in NBG Set Theory 155
Appendix 3. Theorems Proved in Peano s Arithmetic 184
Bibliography 259
Index of Names 267
Index of Subjects 269
|
| any_adam_object | 1 |
| author | Quaife, Art |
| author_facet | Quaife, Art |
| author_role | aut |
| author_sort | Quaife, Art |
| author_variant | a q aq |
| building | Verbundindex |
| bvnumber | BV008048236 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.9.A96 |
| callnumber-search | QA76.9.A96 |
| callnumber-sort | QA 276.9 A96 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 |
| classification_tum | DAT 706f |
| ctrlnum | (OCoLC)26722530 (DE-599)BVBBV008048236 |
| 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 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01734nam a2200457 cb4500</leader><controlfield tag="001">BV008048236</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100805 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">930720s1992 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792320212</subfield><subfield code="9">0-7923-2021-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)26722530</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV008048236</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><subfield code="a">DE-29T</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA76.9.A96</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3</subfield><subfield code="2">20</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="084" ind1=" " ind2=" "><subfield code="a">DAT 706f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Quaife, Art</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Automated development of fundamental mathematical theories</subfield><subfield code="c">by Art Quaife</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht [u.a.]</subfield><subfield code="b">Kluwer</subfield><subfield code="c">1992</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 271 S.</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">Automated reasoning series</subfield><subfield code="v">2</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Künstliche Intelligenz</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Artificial intelligence</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Automatic theorem proving</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Automatisches Beweisverfahren</subfield><subfield code="0">(DE-588)4069034-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Automatisches Beweisverfahren</subfield><subfield code="0">(DE-588)4069034-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Automatisches Beweisverfahren</subfield><subfield code="0">(DE-588)4069034-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-188</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Automated reasoning series</subfield><subfield code="v">2</subfield><subfield code="w">(DE-604)BV004807212</subfield><subfield code="9">2</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ 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=005295687&sequence=000002&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:BVB01-005295687</subfield></datafield></record></collection> |
| id | DE-604.BV008048236 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:13:29Z |
| institution | BVB |
| isbn | 0792320212 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005295687 |
| oclc_num | 26722530 |
| open_access_boolean | |
| owner | DE-739 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-188 |
| owner_facet | DE-739 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | XVIII, 271 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Kluwer |
| record_format | marc |
| series | Automated reasoning series |
| series2 | Automated reasoning series |
| spelling | Quaife, Art Verfasser aut Automated development of fundamental mathematical theories by Art Quaife Dordrecht [u.a.] Kluwer 1992 XVIII, 271 S. txt rdacontent n rdamedia nc rdacarrier Automated reasoning series 2 Künstliche Intelligenz Artificial intelligence Automatic theorem proving Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 s DE-604 Mathematik (DE-588)4037944-9 s DE-188 Automated reasoning series 2 (DE-604)BV004807212 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005295687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Quaife, Art Automated development of fundamental mathematical theories Automated reasoning series Künstliche Intelligenz Artificial intelligence Automatic theorem proving Automatisches Beweisverfahren (DE-588)4069034-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4069034-9 (DE-588)4037944-9 |
| title | Automated development of fundamental mathematical theories |
| title_auth | Automated development of fundamental mathematical theories |
| title_exact_search | Automated development of fundamental mathematical theories |
| title_full | Automated development of fundamental mathematical theories by Art Quaife |
| title_fullStr | Automated development of fundamental mathematical theories by Art Quaife |
| title_full_unstemmed | Automated development of fundamental mathematical theories by Art Quaife |
| title_short | Automated development of fundamental mathematical theories |
| title_sort | automated development of fundamental mathematical theories |
| topic | Künstliche Intelligenz Artificial intelligence Automatic theorem proving Automatisches Beweisverfahren (DE-588)4069034-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Künstliche Intelligenz Artificial intelligence Automatic theorem proving Automatisches Beweisverfahren Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005295687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004807212 |
| work_keys_str_mv | AT quaifeart automateddevelopmentoffundamentalmathematicaltheories |