Nonmonotonic inconsistency

Charles B. Cross
2003 Artificial Intelligence  
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
more » ... onic 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. In classical logic, the concept of logical consequence is correlated in a straightforward and familiar way with the concept of logical inconsistency. And, like logical consequence, logical inconsistency is monotonic. That is, just as condition MLC below holds for logical consequence, so condition MLI holds for logical inconsistency: 1 E-mail address: ccross@uga.edu (C.B. Cross). URL: http://www.phil.uga.edu/faculty/cross/ (C.B. Cross). 1 We shall use p and q to range over sentences and X and Y to range over sets of sentences. We shall use the expression 'X ' to mean that X is logically inconsistent.
doi:10.1016/s0004-3702(03)00074-2 fatcat:5wzp2lmfkjazhll2as5sw3spk4