STABLE SEMANTICS FOR PROBABILISTIC DEDUCTIVE DATABASES

In this paper we study the semantics of non-monotonic negation in prob abilistic deductive databases. Based on the stable semantics for class ical logic programming, we examine three natural notions of stability: stable formula functions, stable families of probabilistic interpreta tions, and stable probabilistic models. We show that stable formula fu nctions are minimal fixpoints of operators associated with probabilist ic logic programs. We also prove that each member in a stable family o f probabilistic interpretations is a probabilistic model of the progra m. Then we show that stable formula functions and stable families beha ve as duals of each other, tying together elegantly the fixpoint and m odel theories for probabilistic logic programs with negation. Furtherm ore, since a probabilistic logic program may not necessarily have a st able family of probabilistic interpretations, we provide a stable clas s semantics for such programs. Finally, we investigate the notion of s table probabilistic model. We show that this notion, though natural, i s too weak in the probabilistic framework. (C) 1994 Academic Press, In c.