The Structure and Complexity of Credal Semantics

A flexible semantics has been proposed by Lukasiewicz for probabilistic logic programs where we have a normal logic program augmented with a set of independent probabilistic facts. That semantics, which we call credal semantics, is the set of all probability measures (over stable models) that are consistent with a total choice of probabilistic facts. When each total choice produces a definite program, credal semantics is identical to Sato’s distribution semantics. However, credal semantics is also defined for programs with cycles and negations. We show that the credal semantics always defines a set containing the probability measures that dominate an infinite monotone Choquet capacity (also known as a belief function). We also show how this result leads to inference algorithms and to an analysis of the complexity of inferences.