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Qualitative conditioning in an interval-based possibilistic setting. (English) Zbl 1397.03033
Summary: Possibility theory and possibilistic logic are well-known uncertainty frameworks particularly suited for representing and reasoning with uncertain, partial and qualitative information. Belief update plays a crucial role when updating beliefs and uncertain pieces of information in the light of new evidence. This paper deals with conditioning uncertain information in a qualitative interval-valued possibilistic setting. The first important contribution concerns a set of three natural postulates for conditioning interval-based possibility distributions. We show that any interval-based conditioning satisfying these three postulates is necessarily based on the set of compatible standard possibility distributions. The second contribution consists in a proposal of efficient procedures to compute the lower and upper endpoints of the conditional interval-based possibility distribution while the third important contribution provides a syntactic counterpart of conditioning interval-based possibility distributions in case where these latter are compactly encoded in the form of possibilistic knowledge bases.
MSC:
03B52 Fuzzy logic; logic of vagueness
68T37 Reasoning under uncertainty in the context of artificial intelligence
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