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Probabilistic reasoning under coherence in System P. (English) Zbl 1014.68165

Summary: We apply a probabilistic reasoning under coherence to System P. We consider a notion of strict probabilistic consistency, we show its equivalence to Adams’ probabilistic consistency, and we give a necessary and sufficient condition for probabilistic entailment. We consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our coherence-based approach, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, obtaining the precise probability bounds for the derived conclusions of the inference rules. This allows a more flexible and realistic use of System P in default reasoning and provides an exact illustration of the degradation of the inference rules when interpreted in probabilistic terms. We also examine the disjunctive Weak Rational Monotony rule of System P\(^+\) proposed by Adams in his extended probabilistic logic. Finally, we examine the propagation of lower bounds with real \(\varepsilon\)-values and, to illustrate our probabilistic reasoning, we consider an example.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
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