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The paper introduces the notion of off-line justification for Answer Set Programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom w.r.t. a given answer set. The notion of justification accounts for the specifics of answer set semantics. 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 on-line justifications within the computation model of Smodels. Justifications offer a basic data structure to support methodologies and tools for debugging answer set programs. A preliminary implementation has been developed in $\mathbb{ASP-PROLOG}$.

Justifications for Logic Programs Under Answer Set Semantics