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RESEARCH PRODUCT
Probabilistic entailment in the setting of coherence: The role of quasi conjunction and inclusion relation
Giuseppe SanfilippoAngelo Giliosubject
FOS: Computer and information sciencesClass (set theory)Goodman–Nguyen’s inclusion relationQAND ruleSettore MAT/06 - Probabilita' E Statistica MatematicaComputer Science - Artificial IntelligenceMathematics - Statistics TheoryStatistics Theory (math.ST)Logical consequencegoodman-nguyen's inclusion relationTheoretical Computer ScienceArtificial IntelligenceQuasi conjunctionFOS: MathematicsEquivalence (measure theory)MathematicsEvent (probability theory)Discrete mathematicsSettore INF/01 - InformaticaApplied MathematicsProbability (math.PR)quasi conjunction; goodman-nguyen inclusion relation; qand rule; coherence; probabilistic default reasoning; p-entailment; goodman-nguyen's inclusion relationProbabilistic logicCoherence (statistics)Conjunction (grammar)Greatest elementArtificial Intelligence (cs.AI)Probabilistic default reasoninggoodman-nguyen inclusion relationp-EntailmentCoherenceSoftwareMathematics - Probabilitydescription
In this paper, by adopting a coherence-based probabilistic approach to default reasoning, we focus the study on the logical operation of quasi conjunction and the Goodman-Nguyen inclusion relation for conditional events. We recall that quasi conjunction is a basic notion for defining consistency of conditional knowledge bases. By deepening some results given in a previous paper we show that, given any finite family of conditional events F and any nonempty subset S of F, the family F p-entails the quasi conjunction C(S); then, given any conditional event E|H, we analyze the equivalence between p-entailment of E|H from F and p-entailment of E|H from C(S), where S is some nonempty subset of F. We also illustrate some alternative theorems related with p-consistency and p-entailment. Finally, we deepen the study of the connections between the notions of p-entailment and inclusion relation by introducing for a pair (F,E|H) the (possibly empty) class K of the subsets S of F such that C(S) implies E|H. We show that the class K satisfies many properties; in particular K is additive and has a greatest element which can be determined by applying a suitable algorithm.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-01 |