Enumerating minimal explanations by minimal hitting set computation

Authors:
Ken Satoh;Takeaki Uno
Affiliations:
National Institute of Informatics and Sokendai;National Institute of Informatics and Sokendai
Venue:
KSEM'06 Proceedings of the First international conference on Knowledge Science, Engineering and Management
Year:
2006

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Abstract

We consider the problem of enumerating minimal explanations in propositional theory. We propose a new way of characterizing the enumeration problem in terms of not only the number of explanations, but also the number of unexplanations. Maximal unexplanations are a maximal set of abducible formulas which cannot explain the observation given a background theory. In this paper, we interleavingly enumerate not only minimal explanations but also maximal unexplanations. To best of our knowledge, there has been no algorithm which is characterized in terms of such maximal unexplanations. We propose two algorithms to perform this task and also analyze them in terms of query complexity, space complexity and time complexity.