Comparing Consequence Relations
نویسنده
چکیده
The technical problem addressed in this paper is, given two rule systems for consequence relations X and Y, how to construct Y-approximations of a given X-relation. While an upper Yapproximation can be easily constructed if all Yrules are Horn, the construction of lower Yapproximations is less straightforward. We address the problem by defining the notion of coclosure under co-Horn rules, that can be used to remedy violation of certain rules by removing arguments. In particular, we show how the coclosure under Monotonicity can be used to construct the monotonic restriction of a preferential relation. Unlike the more usual closure under the rules of M , this co-closure operator supports the intuition that preferential reasoning is more liberal than monotonic reasoning. The approach is embedded in a general framework for comparing rule systems for consequence relations. A salient feature of this framework is that it is also possible to compare rule systems that are not related by metalevel entailment.
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