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An algorithm to compute maximal contractions for Horn clauses

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Abstract

In the theory of belief revision, the computation of all maximal subsets (maximal contractions) of a formula set with respect to a set of facts is one of the key problems. In this paper, we try to solve this problem by studying the algorithm to compute all maximal contractions for Horn clauses. First, we point out and prove the conversion relationship between minimal inconsistent subsets of union of the formula set and the set of facts and maximal contractions of the formula set with respect to the set of facts. Second, we prove a necessary condition of a set of Horn clauses to be minimal inconsistent. Then, based on these two conclusions, we propose an interactive algorithm to enumerate all minimal inconsistent subsets of a given set of Horn clauses and a second algorithm to compute maximal contractions from these minimal inconsistent subsets. Finally, we proposed an interactive algorithm to compute maximal contractions for Horn clauses by composing the above two algorithms.

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Authors and Affiliations

  1. State Key Laboratory of Software Development Environment, School of Computer Science and Technology, Beihang University, Beijing, 100191, China

    Jie Luo & Wei Li

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  1. Jie Luo
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  2. Wei Li
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Correspondence to Jie Luo.

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Luo, J., Li, W. An algorithm to compute maximal contractions for Horn clauses. Sci. China Inf. Sci. 54, 244–257 (2011). https://doi.org/10.1007/s11432-010-4172-9

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  • DOI: https://doi.org/10.1007/s11432-010-4172-9

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