Quasi conjunction and inclusion relation in probabilistic default reasoning

Gilio, A; Sanfilippo, G

doi:10.1007/978-3-642-22152-1_42

We study the quasi conjunction and the Goodman & Nguyen inclusion relation for conditional events, in the setting of probabilistic default reasoning under coherence. We deepen two recent results given in (Gilio and Sanfilippo, 2010): the first result concerns p-entailment from a family F of conditional events to the quasi conjunction C(S) associated with each nonempty subset S of F; the second result, among other aspects, 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 the Goodman & Nguyen inclusion relation; in particular, for a pair (F,E|H), we study the class K of the subsets S of F such that C(S) is included in E|H. We show that K is additive and has a greatest element which can be determined by applying a suitable algorithm.

Gilio, A., Sanfilippo, G. (2011). Quasi conjunction and inclusion relation in probabilistic default reasoning. In W. Liu (a cura di), Symbolic and quantitative approaches to reasoning with uncertainty. 11th European Conference, ECSQARU 2011 (pp. 497-508). Berlin : Springer [10.1007/978-3-642-22152-1_42].