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Probabilistic Reasoning Under Coherence in System P

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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 ε-values and, to illustrate our probabilistic reasoning, we consider an example.

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  1. Dipartimento di Metodi e Modelli Matematici, Via A. Scarpa, 16, 00161, Roma, Italy

    Angelo Gilio

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Gilio, A. Probabilistic Reasoning Under Coherence in System P. Annals of Mathematics and Artificial Intelligence 34, 5–34 (2002). https://doi.org/10.1023/A:1014422615720

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