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RESEARCH PRODUCT

Quasi Conjunction and Inclusion Relation in Probabilistic Default Reasoning

Giuseppe SanfilippoAngelo Gilio

subject

Discrete mathematicsClass (set theory)goodman & nguyen inclusion relationSettore MAT/06 - Probabilita' E Statistica MatematicaSettore INF/01 - Informaticap-entailment.; quasi conjunction; goodman & nguyen inclusion relation; qand rule; coherence; probabilistic default reasoning; p-entailmentProbabilistic logicqand ruleprobabilistic default reasoningConsistency (knowledge bases)Coherence (philosophical gambling strategy)p-entailmentCoherence probabilistic default reasoning quasi conjunction Goodman & Nguyen inclusion relation QAND rule p-entailment.coherenceConjunction (grammar)Default reasoningquasi conjunctionGreatest elementAlgorithmEquivalence (measure theory)Mathematics

description

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.

yearjournalcountryeditionlanguage
2011-01-01
https://doi.org/10.1007/978-3-642-22152-1_42