S Colton, A Bundy, and T Walsh. Automatic invention of integer sequences. In Proceedings of the Seventeenth National Conference on Arti cial Intelligence, 2000. Home/Search Document Details and Download
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Making Conjectures about Maple Functions - Colton (2002) Self-citation (Colton) (Correct)
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S Colton, A Bundy, and T Walsh. Automatic invention of integer sequences. In Proceedings of the Seventeenth National Conference on Arti cial Intelligence, 2000.
An Application-based Comparison of Automated Theory Formation and .. - Colton (2000) Self-citation (Colton) (Correct)
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S Colton, A Bundy, and T Walsh. Automatic invention of integer sequences. In Proceedings of the Seventeenth National Conference on Arti cial Intelligence, pages 558-563, 2000. 18
The NumbersWithNames Program - Colton, Dennis Self-citation (Colton) (Correct)
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S Colton, A Bundy, and T Walsh. Automatic invention of integer sequences. In Proceedings of the 17th National Conference on Arti cial Intelligence, pages 558-563, 2000.
Assessing Exploratory Theory Formation Programs - Colton (2000) Self-citation (Colton Bundy Walsh) (Correct)
....the interestingness of a concept. For example, HR chooses to develop concepts with a variety of examples, which means it avoids the above sequence because it only contains one number. Each theory formation program has its own measures for interestingness and we have surveyed five such programs in (Colton, Bundy, Walsh 2000c) and attempted to derive some common approaches to the assessment of interestingness. Heuristic searches based on these measures of interestingness are intended to increase the quality of the theories produced. Assessment of the theories themselves is also usually subjective, and likewise ....
....believed AM had invented a new type of number: those with more divisors than any smaller number. However, these turned out to be highly composite numbers defined much earlier by Ramanujan. We had a similar experience with refactorable numbers, Colton 1999) but have since redeemed the situation, (Colton, Bundy, Walsh 2000b) ffl The overall quality of the theory. This approach involves examining an example theory produced and grading the interestingness of the concepts in the theory. An overall score is then assigned to the theory, based on the average interestingness of the concepts. This is again subjective, and ....
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Colton, S.; Bundy, A.; and Walsh, T. 2000b. Automatic invention of integer sequences. In Proceedings of the Seventeenth National Conference on Artificial Intelligence.
Automated Theorem Discovery: A Future Direction for Theorem Provers - Colton Self-citation (Colton) (Correct)
....over the set of formulae and again, the format of the results could be predicted in advance as the formulae were simple compositions of the multiplication operation. Zhang stated that combinatorial explosion was a major obstacle to overcome, and that future work would involve 1 See [2] 5] [11] and [14] 3 selection of more complex, more interesting conjectures to (attempt to) prove. To our knowledge, this feature has yet to be added to MCS. The program developed by Rajiv Bagai et al. worked in plane geometry and aimed to nd theorems stating that certain idealised diagrams could not ....
.... For instance, HR invented the concept of integers with a prime number of divisors and also conjectured that if the sum of divisors of an integer is prime, then the number of divisors will also be prime (a result we later proved) Details of the application to number theory are given in [8] and [11]. 2 Worked Example Anti Associative Algebras In [9] we wished to show that HR could be used not only for making conjectures (as it did with the integer sequences) but also to discover theorems, by presenting only those conjectures which it had proved with Otter. We wanted to use HR in a ....
S Colton, A Bundy, and T Walsh. Automatic invention of integer sequences. In Proceedings of the Seventeenth National Conference on Articial Intelligence, pages 558-563, 2000.
Mathematics - a new Domain for Datamining? - Colton Self-citation (Colton) (Correct)
....contrast, very little research has been undertaken towards using datamining techniques for knowledge discovery in mathematical databases. To our knowledge, the only such attempt has been our work datamining conjectures from the Encyclopedia of Integer Sequences, as discussed in (Colton 1999) and (Colton, Bundy, Walsh 2000a) Given a sequence of integers, S usually one invented by our HR program (Colton, Bundy, Walsh 1999) we searched through the Encyclopedia to nd others which were (i) subsequences of S (ii) supersequences of S and (iii) disjoint with S. For example, looking for supersequences of the ....
....problem with this approach was not generating conjectures, but pruning those which were uninteresting. For example, looking for supersequences of the perfect numbers as above produces 7710 examples (in 927 seconds on a 500Mhz Pentium processor) The details of the measures for pruning are given in (Colton, Bundy, Walsh 2000a) It suces here to remark that we used: The terms of the sequence: for instance, we often speci ed that there must be at least three terms in the supersequence which are perfect numbers. The de nition of the sequence: for instance, we discarded any supersequences if the de nition ....
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Colton, S.; Bundy, A.; and Walsh, T. 2000a. Automatic invention of integer sequences. In Proceedings of the Seventeenth National Conference on Articial Intelligence.
Theory Formation Applied to Discovery, Learning and Problem Solving - Colton Self-citation (Colton) (Correct)
....less than an hour, HR can produce more than 2000 concepts in number theory and if the user sets di erent starting parameters, the yield of concepts di ers each time HR is run. There is therefore the possibility of HR producing new and genuinely interesting concepts. We explored this possibility in [3] and we summarise this work below. It is dicult to tell in general whether a concept is either new or interesting. In number theory, however, there is an Encyclopedia of Integer Sequences, 10] which contains over 55,000 sequences collected over 35 years by Neil Sloane, with contributions from ....
S Colton, A Bundy, and T Walsh. Automatic invention of integer sequences. In Proceedings of the Seventeenth National Conference on Arti- cial Intelligence, 2000.
The Limits of Model-based Discovery? - Walsh Self-citation (Walsh) (Correct)
....then enriches future concept formation as concepts and conjectures concerning non Abelian groups can now be made. HR has been very successful, discovering a number of integer sequences which are interesting and novel enough to have been accepted into the Encyclopedia of Integer Sequences [CBW00]. Whilst there are several reasons for this success, one of the most important is that HR is highly model driven. New concepts are made from old ones by forward chaining with a small number of production rules. To control the combinatorial explosion that results, concepts are assessed for their ....
S. Colton, A. Bundy, and T. Walsh. Automatic invention of integer sequences. In Proceedings of the 17th National Conference on AI. American Association for Artificial Intelligence, 2000.
A Challenge for Mechanized Deduction - Benzmüller, Kerber (Correct)
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Simon Colton, Alan Bundy, and Toby Walsh. Automatic invention of integer sequences. In Henry Kautz and Bruce Porter, editors, AAAI-2000, Austin, Texas, USA, 2000. AAAI Press, MIT Press.
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