Abstract
We provide a precise illustration of what can be the idea of “computational creativity”, that is, the whole set of the methods by which a computer may simulate creativity. This paper is restricted to multiple predicate learning in Inductive Logic Programming (ILP) and to Program Synthesis from its Formal Specification (PSFS). These two subfields of Computer Science deal with problems where creativity is of primary importance. They had to add to their basic formalisms, ILP and Beth’s tableaux (for PSFS), sets of heuristics enabling the program to solve the problem of Multiple Predicate synthesis. Some of these are what is usually called a heuristic, that is, a method by which the execution speed of the program is supposed to be boosted, at the price of a lost of some solutions. This paper, inversely, shows heuristics the goal of which is to provide the program with some kind of inventiveness. The basic tool for computational creativity is what we call an ’asset generator’ a specification of which is given in section 4, followed by a detailed description of our methodology for the generation of assets in PSFS. Since it may seem that our ’asset generation methodology’ for PSFS relies essentially on making explicit the logician’s good sense while performing a recursion constructive proof, and as an example of its efficiency, we provide in conclusion a result, a kind of challenge for the other theorem provers, namely: ‘invent’ a form of the Ackerman function which is recursive with respect to the second variable instead of the first variable as the usual definitions are.
In ILP multiple predicate synthesis, the assets have been provided by members of the ILP community, while our methodology tries to make explicit a way to discover these assets when they are needed.
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References
Ade, H., Denecker, M.: AILP: Abductive inductive logic programming. In: Proceedings of the fourteenth International Joint Conference on Artificial Intelligence, pp. 1201–1207 (1995)
Baroglio, C., Botta, M.: Multiple Predicate Learning with RTL. In: Gori, M., Soda, G. (eds.) AI*IA 1995. LNCS, vol. 992, pp. 44–55. Springer, Heidelberg (1995)
Beth, E.: The Foundations of Mathematics, Amsterdam (1959)
Boden, M.: Computational models of creativity. In: Sternberg, R.J. (ed.) Handbook of Creativity, pp. 351–373. Cambridge University Press, Cambridge (1999)
Brazdil, P., Jorge, A.: Learning by Refining Algorithm Sketches. In: ECAI 1994, 11th European Conference of Artificial Intelligence, pp. 427–433 (1994)
De Raedt, L., Lavrac, N., Dzeroski, S.: Multiple Predicate Learning. In: Proceedings of the thirteenth International Joint Conference on Artificial Intelligence, pp. 1037–1042 (1993a)
De Raedt, L., Lavrac, N., Dzeroski, S.: Multiple Predicate Learning. In: Proceedings of the third International Workshop on Inductive Logic Programming, pp. 221–240 (1993b)
De Raedt, L., Lavrac, N.: Multiple Predicate Learning in Two Inductive Logic Programming Settings. J. of the IGPL 4(2), 227–254 (1996)
Esposito, F., Malerba, D., Lisi, F.A.: Multiple Predicate Learning for Document Image Understanding. In: Proceedings of the Fourteenth American Association for Artificial Intelligence Conference, pp. 372–376 (2000)
Fogel, L., Zaverucha, G.: Normal Programs and Multiple Predicate Learning. In: Page, D.L. (ed.) ILP 1998. LNCS, vol. 1446, pp. 175–184. Springer, Heidelberg (1998)
Franova, M.: CM-strategy: A Methodology for Inductive Theorem Proving or Constructive Well-Generalized Proofs. In: Joshi, A.K. (ed.) Proceedings of the Ninth International Joint Conference on Artificial Intelligence, Los Angeles, August 1985, pp. 1214–1220 (1985)
Franova, M.: PRECOMAS - An Implementation of Constructive Matching Methodology. In: Proceedings of ISSAC 1990, Tokyo, Japan, August 20-24, pp. 16–23. ACM, New York (1990)
Franova, M., Kodratoff, Y., Gross, M.: Constructive Matching Methodology: Formally Creative or Intelligent Inductive Theorem Proving? In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS (LNAI), vol. 689, pp. 476–485. Springer, Heidelberg (1993)
Franova, M.: A Construction of a Definition Recursive with respect to the Second Variable for the Ackermann function. To appear as LRI internal research report, Orsay, France (2008)
Giordana, A., Saitta, L., Baroglio, C.: Learning simple recursive theories. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS (LNAI), vol. 689, pp. 425–444. Springer, Heidelberg (1993)
Heitz, T.: Une méthode récursive pour le prétraitement des textes. Thèse, Universite Paris-Sud (2008)
Jorge, A., Brazdil, P.: Architecture for iterative learning of recursive definitions. In: Advances in Inductive Logic Programming, pp. 206–218 (1996)
Kakas, A., Lamma, E., Riguzzi, F.: Learning multiple predicates. In: Giunchiglia, F. (ed.) AIMSA 1998. LNCS (LNAI), vol. 1480, pp. 303–316. Springer, Heidelberg (1998)
Kijsirikul, B., Numao, M., Shimura, M.: Efficient learning of logic programs with non-determinate non-discrimonating literals. In: Kaufmann (ed.) ML 1991 – Machine Learning Conference, pp. 417–421 (1991)
Kijsirikul, B., Numao, M., Shimura, M.: Discrimination-based constructive induction of logic programs. In: Proceedings of the tenth National Joint Conference on Machine Learning, San Jose, CA, pp. 44–49 (1992)
Kleene, S.C.: Introduction to Meta-Mathematics. North-Holland, Amsterdam (1980)
Malerba, D., Esposito, F., Lisi, F.A.: Learning Recursive Theories with ATRE. In: Proceedings of the Thirteenth European Conference on Artificial Intelligence, pp. 435–439 (1998)
Martin, L., Vrain, C.: MULT_ICN: An empirical multiple predicate learner. In: Proc. 5th International Workshop on ILP, pp. 129–144 (1995)
Newell, A., Simon, H.A.: Human Problem Solving. Prentice-Hall, Englewood Cliffs (1972)
Pazzani, M., Kibler, D.: The Utility of Knowledge in Inductive Learning. Machine Learning 9, 57–94 (1992)
Peter, R.: Recursive Functions. Academic Press, New York (1967)
Richards, B.L., Mooney, R.J.: Learning Relations by Pathfinding. In: Proceedings of the Tenth National Conference on Artificial Intelligence. MIT Press, Cambridge (1992)
Yashuhara, A.: Recursive Function Theory and Logic. Academic Press, London (1971)
Zelle, J.M., Mooney, R.J., Konvisser, J.B.: Combining Top-down and Bottom-up Techniques in Inductive Logic Programming. In: Machine Learning: Proceedings of the Eleventh International Conference, pp. 343–351 (1994)
Zhang, X., Numao, M.: MPL-Core: An Efficient Multiple Predicate Learner Based on Fast Failure Mechanism. Journal of Japanese Society for Artificial Intelligence 12(4), 582–590 (1997)
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Fraňová, M., Kodratoff, Y. (2010). Two Examples of Computational Creativity: ILP Multiple Predicate Synthesis and the ‘Assets’ in Theorem Proving. In: Koronacki, J., Raś, Z.W., Wierzchoń, S.T., Kacprzyk, J. (eds) Advances in Machine Learning II. Studies in Computational Intelligence, vol 263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05179-1_8
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