Specifying Transactions for Extended Abduction

Extended abduction introduced by Inoue and Sakama ( 1995 ) generalizes traditional abduction in the sense that it can compute negative explanations by removing hypotheses from a nonmonotonic background theory, rather than only adding them. Also, it has a mechanism of computing anti-explanations to unexplain negative observations. Such extended abduction not only enhances reasoning ability of traditional abduction but has useful applications to nonmonotonic theory change. In this paper, we study the computational aspect of extended abduction. Given a background theory written in nonmonotonic logic programming, we introduce its transaction program for computing extended abduction. A transaction program is a set of nondeterministic production rules that specify addition and deletion of abductive hypotheses. Abductive explanations are computed by the xpoint of a transaction program using a bottom-up model generation procedure. In the context of databases, a transaction program provides a declarative speci cation of database update.