We present a systematic approach for extending the KLM framework for defeasible entailment. We first present a class of basic defeasible entailment relations, characterise it in three distinct ways and provide a high-level algorithm for computing it. This framework is then refined, with the refined version being characterised in a similar manner. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic closure, fall within our refined framework, that rational closure is the most conservative of the defeasible entailment relations within the framework (with respect to subset inclusion), but that there are forms of defeasible entailment within our framework that are more "adventurous" than lexicographic closure.
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