New Results for Horn Cores and Envelopes of Horn Disjunctions

Authors:
Thomas Eiter;Kazuhisa Makino
Affiliations:
Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria, eiter@kr.tuwien.ac.at;Graduate School of Information Science and Technology, University of Tokyo, Tokyo, 113-8656, Japan, makino@mist.i.u-tokyo.ac.jp
Venue:
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Year:
2008

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Abstract

We provide a characterization of Horn cores for formulas in conjunctive normal form (CNF) and, based on it, a novel algorithm for computing Horn cores of disjunctions of Horn CNFs that has appealing properties (e.g., it is polynomial for a bounded disjunction). Furthermore, we show that recognizing the Horn envelope of a disjunction of two Horn CNFs is intractable, and that computing a compact Horn CNF for it (that is irredundant and prime) is not feasible in polynomial total time unless P=NP; this answers an open problem.