In answer set programming, inconsistencies arise when the constraints placedon a program become unsatisfiable. In this paper, we introduce a technique fordynamic consistency checking for our goal-directed method for computing answersets, under which only those constraints deemed relevant to the partial answerset are tested, allowing inconsistent knowledgebases to be successfullyqueried. However, the algorithm guarantees that, if a program has at least oneconsistent answer set, any partial answer set returned will be a subset of someconsistent answer set. To appear in Theory and Practice of Logic Programming(TPLP).
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