Nonmonotonic Inconsistency

Artificial Intelligence 149 (2):161-178 (2003)
Nonmonotonic consequence is the subject of a vast literature, but the idea of a nonmonotonic counterpart of logical inconsistency—the idea of a defeasible property representing internal conflict of an inductive or evidential nature—has been entirely neglected. After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic inconsistency, an analysis of nonmonotonic inconsistency in terms of nonmonotonic consequence, and a series of results showing that nonmonotonic inconsistency conforms to these postulates given the analysis of nonmonotonic inconsistency presented here and certain postulates for nonmonotonic consequence. The results presented here establish the interest of certain previously undiscussed postulates of nonmonotonic consequence. These results also show that nonmonotonicity, which has never seemed useful in the formulation of general principles governing nonmonotonic reasoning, is relevant to the positive characterization of nonmonotonic inference after all.
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