Link to this article: http://journals.cambridge.org/abstract_S1471068408003633How to cite this article: ENRICO PONTELLI, TRAN CAO SON and OMAR ELKHATIB (2009). Justications for logic programs under answer set semantics.
AbstractThe 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 ASP − PROLOG.Proof. The result is obvious from the definition of offline e-graph and from the fact that J − ∩ TA P (M) ⊆ TA P (M). Proposition 4. Let M 0 , . . . , M k be a general complete computation and S(M 0 ), . . . , S(M k ) be an online justification of the computation. Then, for each atom a in M k , the egraph of a in S(M k ) is an offline justification of a w.r.t. M k and TA P (M k ).Proof. This follows immediately from Lemma 5.2, the construction of the snapshots S(M i ), the fact that M i M k for every k, and M k being an answer set of P .