Automated Theory Formation in Pure Mathematics:
In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory forma...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Springer London
2002
|
| Ausgabe: | 1st ed. 2002 |
| Schriftenreihe: | Distinguished Dissertations
|
| Schlagworte: | |
| Online-Zugang: | UBY01 Volltext |
| Zusammenfassung: | In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians |
| Beschreibung: | 1 Online-Ressource (XVI, 380 p) |
| ISBN: | 9781447101475 |
| DOI: | 10.1007/978-1-4471-0147-5 |
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| discipline | Informatik Mathematik |
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| doi_str_mv | 10.1007/978-1-4471-0147-5 |
| edition | 1st ed. 2002 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:12:21Z |
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| isbn | 9781447101475 |
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| spelling | Colton, Simon Verfasser aut Automated Theory Formation in Pure Mathematics by Simon Colton 1st ed. 2002 London Springer London 2002 1 Online-Ressource (XVI, 380 p) txt rdacontent c rdamedia cr rdacarrier Distinguished Dissertations In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians Mathematics, general Artificial Intelligence Math Applications in Computer Science Mathematics Artificial intelligence Computer science—Mathematics Programm (DE-588)4047394-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Mathematik (DE-588)4037944-9 s Theorie (DE-588)4059787-8 s Programm (DE-588)4047394-6 s DE-604 Erscheint auch als Druck-Ausgabe 9781447111139 Erscheint auch als Druck-Ausgabe 9781852336097 Erscheint auch als Druck-Ausgabe 9781447101482 https://doi.org/10.1007/978-1-4471-0147-5 Verlag URL des Eerstveröffentlichers Volltext |
| spellingShingle | Colton, Simon Automated Theory Formation in Pure Mathematics Mathematics, general Artificial Intelligence Math Applications in Computer Science Mathematics Artificial intelligence Computer science—Mathematics Programm (DE-588)4047394-6 gnd Mathematik (DE-588)4037944-9 gnd Theorie (DE-588)4059787-8 gnd |
| subject_GND | (DE-588)4047394-6 (DE-588)4037944-9 (DE-588)4059787-8 |
| title | Automated Theory Formation in Pure Mathematics |
| title_auth | Automated Theory Formation in Pure Mathematics |
| title_exact_search | Automated Theory Formation in Pure Mathematics |
| title_exact_search_txtP | Automated Theory Formation in Pure Mathematics |
| title_full | Automated Theory Formation in Pure Mathematics by Simon Colton |
| title_fullStr | Automated Theory Formation in Pure Mathematics by Simon Colton |
| title_full_unstemmed | Automated Theory Formation in Pure Mathematics by Simon Colton |
| title_short | Automated Theory Formation in Pure Mathematics |
| title_sort | automated theory formation in pure mathematics |
| topic | Mathematics, general Artificial Intelligence Math Applications in Computer Science Mathematics Artificial intelligence Computer science—Mathematics Programm (DE-588)4047394-6 gnd Mathematik (DE-588)4037944-9 gnd Theorie (DE-588)4059787-8 gnd |
| topic_facet | Mathematics, general Artificial Intelligence Math Applications in Computer Science Mathematics Artificial intelligence Computer science—Mathematics Programm Mathematik Theorie |
| url | https://doi.org/10.1007/978-1-4471-0147-5 |
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