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Comparing consequence relations

Peter A. Flach, Comparing consequence relations. Proceedings of the Third Dutch/German Workshop on Nonmonotonic Reasoning Techniques and their Applications. ISSN 0946-011X, pp. 130–138. January 1997. No electronic version available.

Abstract

It is often said that the essential feature of non-monotonic reasoning is `jumping to conclusions', i.e. inferring more than is deductively implied. However, the relation between nonmonotonic rea-soning and deductive reasoning has not been thor-oughly investigated, and the few results that exist seem to suggest that nonmonotonic reasoning is actually less liberal than deductive reasoning. For in-stance, Kraus et al. [1990] define a closure operator that turns any given preferential consequence rela-tion into a monotonic extension. In this paper we define a co-closure operator that turns a preferential relation into its monotonic restriction. This demonstrates that the relation between preferential and monotonic reasoning is inherently ambiguous, since there are two ways of turning a preferential relation into a monotonic relation: restricting it by dropping the defaults, or extending it by dropping the exceptions. This result is embedded in a general framework for comparing consequence relations, in which it is also possible to compare rule systems that are not related by metalevel entailment.

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