Mathematical applications of inductive logic programming

Machine Learning

Volumn 64, Issue 1-3, 2006, Pages 25-64

  Colton, Simon ^a   Muggleton, Stephen ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; FUNCTIONS; INFORMATION SCIENCE; INFORMATION TECHNOLOGY; LEARNING SYSTEMS; NUMERICAL METHODS; THEOREM PROVING;

ALGEBRAIC PROPERTIES; COMPUTER ALGEBRA SYSTEMS; GRAFFITI PROGRAMS; INDUCTIVE LOGIC PROGRAMMING (ILP);

LOGIC PROGRAMMING;

EID: 33748258488     PISSN: 08856125     EISSN: 15730565     Source Type: Journal    
DOI: 10.1007/s10994-006-8259-x     Document Type: Conference Paper

References (44)

1. Abell, M., & Braselton, J. (1994). Maple V by example. Associated Press Professional.
2. Brachman, R., & Levesque, H. (Eds.), (1985). Readings in knowledge representation. Morgan Kaufmann.
3. Caporossi, G., & Hansen, P. (1999), Finding relations in polynomial time. In: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence.
4. Colton, S. (1999). Refactorable numbers - a machine invention. Journal of Integer Sequences, 2.
5. Colton, S. (2000). An application-based comparison of automated theory formation and inductive logic programming. Electronic Transactions in Artificial Intelligence, 4(B).
6. Colton, S. (2002a). Automated theory formation applied to mutagenesis data. In: Proceedings of the First British-Cuban Workshop on BioInformatics.
7. Colton, S. (2002b). Automated theory formation in pure mathematics. Springer-Verlag.
8. Colton, S. (2002c). The HR program for theorem generation. In: Proceedings of the Eighteenth Conference on Automated Deduction.
9. Colton, S. (2002d). Making conjectures about maple functions. In: Proceedings of the Tenth Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, LNAI 2385. Springer-Verlag.
10. Colton, S. (2003). ILP for mathematical discovery In: Proceedings of the Thirteenth International Conference on Inductive Logic Programming.
11. Colton, S., Bundy, A., & Walsh, T. (2000a). Automatic identification of mathematical concepts. In: Machine Learning: Proceedings of the Seventeenth International Conference.
12. Colton, S., Bundy, A., & Walsh, T. (2000b). Automatic invention of integer sequences. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence.
13. Colton, S., Bundy, A., & Walsh, T. (2000c). On the notion of interestingness in automated mathematical discovery. International Journal of Human Computer Studies, 53(3), 351-375.
14. Colton, S., & Dennis, L. (2002). The NumbersWithNames Program. In: Proceedings of the Seventh AI and Maths Symposium.
15. Colton, S., & Huczynska, S. (2003). The HOMER system. In: Proceedings of the Nineteenth International Conference on Automated Deduction (LNAI 2741). (pp. 289-294).
16. Colton, S., Meier, A., Sorge, V., & McCasland, R. (2004). Automatic generation of classification theorems for finite algebras. In: Proceedings of the International Joint Conference on Automated Reasoning.
17. Colton, S., Miguel, I. (2001). Constraint generation via automated theory formation. In: Proceedings of CP-01.
18. Colton, S., Pease, A. (2003). Lakatos-style methods in automated reasoning. In: Proceedings of the IJCAI'03 Workshop on Agents and Reasoning.
19. Colton, S., & Pease, A. (2004). The TM system for repairing non-theorems. In: Proceedings of the IJCAR'04 Disproving Workshop.
20. Colton, S., & Sutcliffe, G. (2002). Automatic generation of benchmark problems for automated theorem proving systems. In: Proceedings of the Seventh AI and Maths Symposium.
21. Conway, J. (1976). On numbers and games. Academic Press.
22. De Raedt, L., & Dehaspe, L. (1997). Clausal discovery. Machine Learning, 26, 99-146.
23. Dehaspe, L., & Toivonen, H. (1999). Discovery of frequent datalog patterns. Data Mining and Knowledge Discovery, 3(1), 7-36.
24. Epstein, S. (1988). Learning and discovery: One system's search for mathematical knowledge. Computational Intelligence, 4(1), 42-53.
25. Fajtlowicz, S. (1988). On conjectures of Graffiti. Discrete Mathematics, 72, (23), 113-118.
26. Franke, A., & Kohlhase, M. (1999). System description: MATHWEB, an agent-based communication layer for distributed automated theorem proving. In: Proceedings of the Sixteenth Conference on Automated Deduction, (pp. 217-221).
27. Gap (2000). GAP reference manual. The GAP Group, School of Mathematical and Computational Sciences, University of St. Andrews.
28. Humphreys, J. (1996). A Course in group theory. Oxford University Press.
29. Jackson, P. (1992). Computing prime implicates incrementally. In: Proceedings of CADE 11.
30. Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge University Press.
31. Lenat, D. (1982). AM: discovery in mathematics as heuristic search. In: D. Lenat and R. Davis (Eds.), Knowledge-based systems in artificial intelligence. McGraw-Hill Advanced Computer Science Series.
32. McCune, W. (1990). The OTTER user's guide. Technical Report ANL/90/9, Argonne National Laboratories.
33. McCune, W. (1994). A Davis-Putnam program and its application to finite first-order model search. Technical Report ANL/MCS-TM-194, Argonne National Laboratories.
34. Meier, A., Sorge, V., & Colton, S. (2002). Employing theory formation to guide proof planning. In: Proceedings of the Tenth Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, LNAI 2385. Springer-Verlag.
35. Mohamadali, N. (2003). A Rational reconstruction of the graffiti program. Master's thesis, Department of Computing, Imperial College, London.
36. Muggleton, S. (1995). Inverse entailment and Progol. New Generation Computing, 13, 245-286.
37. Quinlan, R. (1993). C4.5: Programs for machine learning. Morgan Kaufmann.
38. Sims, M., & Bresina, J. (1989). Discovering mathematical operator definitions. In: Machine Learning: Proceedings of the Sixth International Conference. Morgan Kaufmann.
39. Sloane, N. (2000). The online encyclopedia of integer sequences, http://www.research.att.com/~njas/sequences.
40. Srinivasan, A., Muggleton, S., King, R., & Sternberg, M. (1996). Theories for mutagenicity: A study of first-order and feature based induction'. Artificial Intelligence, 85(1, 2), 277-299.
41. Steel, G. (1999). Cross domain concept formation using HR. Master's thesis, Division of Informatics, University of Edinburgh.
42. Sutcliffe, G., & Suttner, C. (1998). The TPTP problem library: CNF release vl.2.1'. Journal of Automated Reasoning, 21(2), 177-203.
43. Weidenbach, C. (1999). SPASS: Combining superposition, sorts and splitting. In: R. A and V. A (Eds.), Handbook of automated reasoning. Elsevier Science.
44. Zimmer, J., Franke, A., Colton, S., & Sutcliffe, G. (2002). Integrating HR and tptp2x into MathWeb to compare automated theorem provers. In: Proceedings of the CADE'02 Workshop on Problems and Problem sets.