Quasi Conjunction and Inclusion Relation in Probabilistic Default Reasoning
نویسندگان
چکیده
We study in the setting of probabilistic default reasoning under coherence the quasi conjunction, which is a basic notion for defining consistency of conditional knowledge bases, and the Goodman & Nguyen inclusion relation for conditional events. We deepen two results given in a previous paper: the first result concerns p-entailment from a finite family F of conditional events to the quasi conjunction C(S), for each nonempty subset S of F ; the second result analyzes the equivalence between p-entailment from F and p-entailment from C(S), where S is some nonempty subset of F . We also characterize p-entailment by some alternative theorems. Finally, we deepen the connections between p-entailment and inclusion relation, by introducing for a pair (F , E|H) the class of the subsets S of F such that C(S) implies E|H . This class is additive and has a greatest element which can be determined by applying a suitable algorithm.
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