Negation as Failure through Abduction: Reasoning about Termination

We study termination properties of normal logic programs where negation as failure is interpreted as a form of abduction, as originally proposed by Eshghi and Kowalski in [EK89]. The abductive proof procedure associated with this interpretation exhibits a better behavior than SLDNF as far as termination is concerned. We first present a strong termination characterization for the Eshghi and Kowalski proof procedure for Datalog programs which is sound and complete. We then extend the characterization to the class of non-Datalog programs, and prove its soundness. Finally we present two instantiations of the general characterization and study the relationships between the classes of programs introduced in the paper.