Abstract
In this paper, we investigate the properties of ordered clauses defined as a sequence of literals. First, we show that while there exists no least generalization of two ordered clauses, every minimal generalization of them has a complete selection to which the result applying Plotkin’s algorithm is subsume-equivalent. Furthermore, we show that the number of complete selections can grow exponentially. Next, we show that the subsumption problem for ordered clauses is also NP-complete as similar as general clauses.
This work is partially supported by Grand-in-Aid for Scientific Research 15700137 and 16016275 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
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References
Baxter, L.D.: The complexity of unification, Doctoral Thesis, Department of Computer Science, University of Waterloo (1977)
Chekuri, C., Rajaraman, A.: Conjunctive query containment revisited. Theoretical Computer Science 239, 211–229 (2000)
Dan Lee, S., De Raedt, L.: Constraint based mining of first order sequences in seqLog. In: Meo, R., Lanzi, P.L., Klemettinen, M. (eds.) Database Support for Data Mining Applications. LNCS (LNAI), vol. 2682, pp. 154–173. Springer, Heidelberg (2004)
Džeroski, S., Muggleton, S., Russell, S.: PAC-learnability of determinate logic programs. In: Proc. 5th COLT, pp. 128–135 (1992)
Garey, M.R., Johnson, D.S.: Computers and intractability: A guide to the theory of NP-completeness. W. H. Freeman and Company, New York (1979)
Gottlob, G., Fermüller, C.G.: Removing redundancy from a clause. Artificial Intelligence 61, 263–289 (1993)
Kietz, J.-U., Džeroski, S.: Inductive logic programming and learnability. SIGART Bulletin 5, 22–32 (1994)
Kietz, J.-U., Lübbe, M.: An efficient subsumption algorithm for inductive logic programming. In: Proc. 11th ICML, pp. 130–138 (1994)
van der Laag, P.R.J.: An analysis of refinement operators in inductive logic programming, Ph.D. Thesis, Tinbergen Institute (1995)
Lassez, J.-L., Maher, M.J., Marriot, L.: Unification revisited. In: Minker, J. (ed.) Foundations of deductive databases and logic programming, pp. 587–625. Morgan Kaufmann, San Francisco (1988)
Lloyd, J.W.: Foundations of logic programming, 2nd extended edn. Springer, Heidelberg (1987)
Nienhuys-Cheng, S.-H., de Wolf, R.: Foundations of Inductive Logic Programming. LNCS (LNAI), vol. 1228. Springer, Heidelberg (1997)
Plotkin, G.D.: A note on inductive generalization. Machine Intelligence 5, 153–163 (1970)
Reynolds, J.C.: Transformational systems and the algebraic structure of atomic formulas. Machine Intelligence 5, 135–152 (1970)
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Kuwabara, M., Ogawa, T., Hirata, K., Harao, M. (2006). On Generalization and Subsumption for Ordered Clauses. In: Washio, T., Sakurai, A., Nakajima, K., Takeda, H., Tojo, S., Yokoo, M. (eds) New Frontiers in Artificial Intelligence. JSAI 2005. Lecture Notes in Computer Science(), vol 4012. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780496_24
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DOI: https://doi.org/10.1007/11780496_24
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