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Journal of Logic and Computation 2000 10(5):705-719; doi:10.1093/logcom/10.5.705
© 2000 by Oxford University Press
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Non-cumulative reasoning: rules and models

J Engelfriet

Faculty of Sciences, Division of Mathematics and Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands E-mail: Joeri_Engelfriet@McKinsey.com

Many abstract studies of non-monotonic consequence relations (such as the one by Kraus, Lehmann and Magidor) have focused on logics which, in addition to satisfying some other properties, are cumulative. A number of concrete non-monotonic logics that have been proposed in the literature, however, are not cumulative. Furthermore, the restriction of smoothness that has to be imposed on preferential models to ensure that their consequence relation satisfies Cautious Monotonicity is a strange condition from an ontological point of view. We argue that cumulativity is not a necessary property for non-monotonic logics, and we will give a number of representation results for non-cumulative consequence relations. This paper thus complements the results of Kraus, Lehmann and Magidor for the non-cumulative case.

Keywords: non-monotonic reasoning, preferential logics, consequence relations, representation, preferential models


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