Abstract
Efficiency of the first-order logic proof procedure is a major issue when deduction systems are to be used in real environments, both on their own and as a component of larger systems (e.g., learning systems). Hence, the need of techniques that can perform such a process with reduced time/space requirements (specifically when performing resolution). This paper proposes a new algorithm that is able to return the whole set of solutions to θ-subsumption problems by compactly representing substitutions. It could be exploited when techniques available in the literature are not suitable. Experimental results on its performance are encouraging.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chang, C.L., Lee, R.C.T.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York (1973)
Eisinger, N.: Subsumption and connection graphs. In: Siekmann, J.H. (ed.) GWAI-81, German Workshop on Artificial Intelligence, Bad Honnef, pp. 188–198. Springer, Berlin (1981)
Ferilli, S., Fanizzi, N., Di Mauro, N., Basile, T.M.A.: Efficient θ-subsumption under Object Identity. In: Atti del Workshop AI*IA su Apprendimento Automatico, Siena - Italy (2002)
Giordana, A., Botta, M., Saitta, L.: An experimental study of phase transitions in matching. In: Thomas, D. (ed.) Proceedings of IJCAI 1999, vol. 2, pp. 1198–1203. Morgan Kaufmann Publishers, San Francisco (1999)
Gottlob, G., Leitsch, A.: On the efficiency of subsumption algorithms. Journal of the Association for Computing Machinery 32(2), 280–295 (1985)
Helft, N.: Inductive generalization: A logical framework. In: Bratko, I., Lavrač, N. (eds.) Progress in Machine Learning, Wilmslow, UK, pp. 149–157. Sigma Press (1987)
Kietz, J.-U., Lübbe, M.: An efficient subsumption algorithm for inductive logic programming. In: Cohen, W., Hirsh, H. (eds.) Proceedings of ICML 1994, pp. 130–138 (1994)
Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, New York (1987)
Maloberti, J., Sebag, M.: θ-subsumption in a constraint satisfaction perspective. In: Rouveirol, C., Sebag, M. (eds.) ILP 2001. LNCS (LNAI), vol. 2157, pp. 164–178. Springer, Heidelberg (2001)
Robinson, J.A.: A machine-oriented logic based on the resolution principle. Journal of the ACM 12(1), 23–49 (1965)
Scheffer, T., Herbrich, R., Wysotzki, F.: Efficient θ-subsumption based on graph algorithms. In: ILP 1996. Lecture Notes in Computer Science(LNAI), vol. 1314, pp. 212–228. Springer, Heidelberg (1997)
Schmidt-Schauss, M.: Implication of clauses is undecidable. Theoretical Computer Science 59, 287–296 (1988)
Srinivasan, A., Muggleton, S., Sternberg, M.J.E., King, R.D.: Theories for mutagenicity: A study in first-order and feature-based induction. Artificial Intelligence 85(1-2), 277–299 (1996)
Stillman, R.B.: The concept of weak substitution in theorem-proving. Journal of ACM 20(4), 648–667 (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ferilli, S., Di Mauro, N., Basile, T.M.A., Esposito, F. (2003). A Complete Subsumption Algorithm. In: Cappelli, A., Turini, F. (eds) AI*IA 2003: Advances in Artificial Intelligence. AI*IA 2003. Lecture Notes in Computer Science(), vol 2829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39853-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-39853-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20119-9
Online ISBN: 978-3-540-39853-0
eBook Packages: Springer Book Archive