Probabilistic Reasoning Under Coherence in System P |
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Authors: | Angelo Gilio |
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Affiliation: | (1) Dipartimento di Metodi e Modelli Matematici, Via A. Scarpa, 16, 00161 Roma, Italy |
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Abstract: | In this paper 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 -values and, to illustrate our probabilistic reasoning, we consider an example. |
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Keywords: | probabilistic reasoning coherence conditional probability bounds precise propagation nonmonotonic reasoning System P probabilistic consistency probabilistic entailment |
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