The paper introduces the notion of offline justification for answer set programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom with respect to a given answer set. The paper extends also this notion to provide justification of atoms during the computation of an answer set (on-line justification) and presents an integration of online justifications within the computation model of Smodels. Offline and online justifications provide useful tools to enhance understanding of ASP, and they offer a basic data structure to support methodologies and tools for debugging answer set programs. A preliminary implementation has been developed in – .

This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give several non-trivial examples and illustrate the use of P-log for knowledge representation and updating of knowledge. We argue that our approach to updates is more appealing than existing approaches. We give sufficiency conditions for the coherency of P-log programs and show that Bayes nets can be easily mapped to coherent P-log programs.