Taking Defeasible Entailment beyond Rational Closure

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.