Home > Mathematics and Science Textbooks > Mathematics > Mathematical foundations > Mathematical logic > Automated Theory Formation in Pure Mathematics: (Distinguished Dissertations)
37%
Automated Theory Formation in Pure Mathematics: (Distinguished Dissertations)

Automated Theory Formation in Pure Mathematics: (Distinguished Dissertations)

          
5
4
3
2
1

Available


Premium quality
Premium quality
Bookswagon upholds the quality by delivering untarnished books. Quality, services and satisfaction are everything for us!
Easy Return
Easy return
Not satisfied with this product! Keep it in original condition and packaging to avail easy return policy.
Certified product
Certified product
First impression is the last impression! Address the book’s certification page, ISBN, publisher’s name, copyright page and print quality.
Secure Checkout
Secure checkout
Security at its finest! Login, browse, purchase and pay, every step is safe and secured.
Money back guarantee
Money-back guarantee:
It’s all about customers! For any kind of bad experience with the product, get your actual amount back after returning the product.
On time delivery
On-time delivery
At your doorstep on time! Get this book delivered without any delay.
Quantity:
Add to Wishlist

About the Book

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.

Table of Contents:
1. Introduction.- 1.1 Motivation.- 1.2 Aims of the Project.- 1.3 Contributions.- 1.4 Organisation of the Book.- 1.5 Summary.- 2. Literature Survey.- 2.1 Some Philosophical Issues.- 2.2 Mathematical Theory Formation Programs.- 2.3 The BACON Programs.- 2.4 Concept Invention.- 2.5 Conjecture Making Programs.- 2.6 The Otter and MACE Programs.- 2.7 The Encyclopedia of Integer Sequences.- 2.8 Summary.- 3. Mathematical Theories.- 3.1 Group Theory, Graph Theory and Number Theory.- 3.2 Mathematical Domains.- 3.3 The Content of Theories.- 3.4 Summary.- 4. Design Considerations.- 4.1 Aspects of Theory Formation.- 4.2 Concept and Conjecture Making Decisions.- 4.3 The Domains HR Works in.- 4.4 Representation Issues.- 4.5 The HR Program in Outline.- 4.6 Summary.- 5. Background Knowledge.- 5.1 Objects of Interest (Entities).- 5.2 Required Information about Concepts.- 5.3 Initial Concepts from the User.- 5.4 Generating Initial Concepts from Axioms.- 5.5 Summary.- 6. Inventing Concepts.- 6.1 An Overview of the Production Rules.- 6.2 The Exists Production Rule.- 6.3 The Match Production Rule.- 6.4 The Negate Production Rule.- 6.5 The Size Production Rule.- 6.6 The Split Production Rule.- 6.7 The Compose Production Rule.- 6.8 The Forall Production Rule.- 6.9 Efficiency and Soundness Considerations.- 6.10 Example Constructions.- 6.11 Summary.- 7. Making Conjectures.- 7.1 Equivalence Conjectures.- 7.2 Implication Conjectures.- 7.3 Non-existence Conjectures.- 7.4 Applicability Conjectures.- 7.5 Conjecture Making Using the Encyclopedia of Integer Sequences.- 7.6 Issues in Automated Conjecture Making.- 7.7 Summary.- 8. Settling Conjectures.- 8.1 Reasons for Settling Conjectures.- 8.2 Proving Conjectures.- 8.3 Disproving Conjectures.- 8.4 Returning to Open Conjectures.- 8.5 Summary.- 9. Assessing Concepts.- 9.1 The Agenda Mechanism.- 9.2 The Interestingness of Mathematical Concepts.- 9.3 Intrinsic and Relational Measures of Concepts.- 9.4 Utilitarian Properties of Concepts.- 9.5 Conjectures about Concepts.- 9.6 Details of the Heuristic Searches.- 9.7 Worked Example.- 9.8 Other Possibilities.- 9.9 Summary.- 10. Assessing Conjectures.- 10.1 Generic Measures for Conjectures.- 10.2 Additional Measures for Theorems.- 10.3 Additional Measures for Non-theorems.- 10.4 Setting Weights for Conjecture Measures.- 10.5 Assessing Concepts Using Conjectures.- 10.6 Worked Example.- 10.7 Summary.- 11. An Evaluation of HR’s Theories.- 11.1 Analysis of Two Theories.- 11.2 Desirable Qualities of Theories — Concepts.- 11.3 Desirable Qualities of Theories — Conjectures.- 11.4 Using the Heuristic Search.- 11.5 Classically Interesting Results.- 11.6 Conclusions.- 12. The Application of HR to Discovery Tasks.- 12.1 A Classification Problem.- 12.2 Exploration of an Algebraic System.- 12.3 Invention of Integer Sequences.- 12.4 Discovery Task Failures.- 12.5 Valdés-Pérez’s Machine Discovery Criteria.- 12.6 Conclusions.- 13. Related Work.- 13.1 A Comparison of HR and the AM Program.- 13.2 A Comparison of HR and the GT Program.- 13.3 A Comparison of HR and the IL Program.- 13.4 A Comparison of HR and Bagai et al’s Program.- 13.5 A Comparison of HR and the Graffiti Program.- 13.6 A Comparison of HR and the Progol Program.- 13.7 Summary.- 14. Further Work.- 14.1 Additional Theory Formation Abilities.- 14.2 The Application of Theory Formation.- 14.3 Theoretical Explorations.- 14.4 Summary.- 15. Conclusions.- 15.1 Have We Achieved Our Aims?.- 15.2 Contributions.- 15.3 Automated Theory Formation in Pure Maths.- Appendix A. User Manual for HR1.11.- Appendix B. Example Sessions.-Appendix C. Number Theory Results.


Best Sellers


Product Details
  • ISBN-13: 9781447111139
  • Publisher: Springer London Ltd
  • Publisher Imprint: Springer London Ltd
  • Edition: Softcover reprint of the original 1st ed. 2002
  • Language: English
  • Returnable: N
  • Spine Width: 21 mm
  • Width: 155 mm
  • ISBN-10: 1447111133
  • Publisher Date: 27 Sep 2012
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 380
  • Series Title: Distinguished Dissertations
  • Weight: 557 gr


Similar Products

How would you rate your experience shopping for books on Bookswagon?

Add Photo
Add Photo

Customer Reviews

REVIEWS           
Click Here To Be The First to Review this Product
Automated Theory Formation in Pure Mathematics: (Distinguished Dissertations)
Springer London Ltd -
Automated Theory Formation in Pure Mathematics: (Distinguished Dissertations)
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Automated Theory Formation in Pure Mathematics: (Distinguished Dissertations)

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book
    Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!
    ASK VIDYA