The Alternating Fixpoint of Logic Programs with Negation

The alternating xpoint of a logic program with negation is de ned constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least xpoint is reached, using a transformation related to the one that de nes stable models. From a xed set of negative conclusions, the positive conclusions follow without deriving any further negative ones, by traditional Horn clause semantics. The union of positive and negative conclusions is called the alternating xpoint partial model. The name alternating" was chosen because the transformation runs in two passes; the rst pass transforms an underestimate of the set of negative conclusions into an intermediate overestimate; the second pass transforms the overestimate into a new underestimate; the composition of the two passes is monotonic. The principal contributions of this work are 1 that the alternating xpoint partial model is identical to the well-founded partial model, and 2 that alternating xpo...

• Type: Conference
• Year: 1989
• Where: PODS
• Authors: Allen Van Gelder
• Keywords: Database, Negative Conclusions, PODS 1989, Xpoint Logic, Xpoint Partial Model