An Abductive Procedure for the CMS/ATMS

This paper concerns procedural semantics for a variety of ATMSs. Reiter & de Kleer view an ATMS as a kind of abduction in which the best explanation of a formula is defined as a minimal conjunction of hypotheses that explain the formula. However, they do not give any algorithm to compute such minimal explanations of a formula in their CMS that is a generalization of de Kleer's basic ATMS. In this paper, we use the notion of characteristic clauses to make precise definitions of the CMS and the ATMS and to produce a sound and complete abductive procedure based on an extension of linear resolution. By means of this abductive procedure, we give the CMS algorithms for computing minimal explanations in the interpreted approach and for updating them in the compiled approach. We then present algorithms for generating and updating labels of nodes in an extended ATMS that accepts non-Horn justifications and literal assumptions. Finally, how a variation of the abductive procedure can be used to answer queries for circumscription of ground theories is presented.

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