A modal perspective on defeasible reasoning
نویسنده
چکیده
We introduce various new supraclassical entailment relations for defeasible reasoning and investigate some of their relationships. The contrapositive of the usual nonmonotonic preferential entailment turns out to be a monotonic supraclassical entailment. Analogously to these two, a nonmonotonic and its contrapositive monotonic supraclassical entailment can be defined by using modal operators relative to a reflexive accessibility relation instead of a preference order. Then again, by using the strict variant of a preference order on worlds as accessibility relation, modal versions of the usual preferential entailment and its contrapositive are obtained. Proof-theoretic aspects of modal preferential entailment is discussed briefly, leading to a characterization of modular Gödel-Löb logics. The link established between preferential and modal logics make existing modal proof and satisfiability algorithms available for use in preferential logics.
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