Abstract

. We propose a technique for dealing with the high complexity of reasoning under propositional default logic and circumscription. The technique is based on the notion of approximation: A logical consequence relation is computed by means of sound and progressively "more complete" relations, as well as complete and progressively "more sound" ones. Both sequences generated in this way converge to the original consequence relation and are easier to compute. Moreover they are given a clear semantics based on multivalued logic. With this technique unsoundness and incompleteness are introduced in a controlled way and precisely characterized. 1 Introduction Default logic [38] and circumscription [34, 35, 33] are the most interesting and wellstudied formalisms for the description of non-monotonic reasoning. A drawback of these formalisms is their high computational complexity. As shown by several authors [6, 27, 44], there are many languages in which inference is polynomial for the monotonic ...

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