On generalization and subsumption for ordered clauses

Authors:
Megumi Kuwabara;Takeshi Ogawa;Kouichi Hirata;Masateru Harao
Affiliations:
Graduate School of Computer Science and Systems Engineering;Graduate School of Computer Science and Systems Engineering;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan
Venue:
JSAI'05 Proceedings of the 2005 international conference on New Frontiers in Artificial Intelligence
Year:
2006

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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.