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.
Probabilistic reasoning under coherence in System P / Gilio, Angelo. - In: ANNALS OF MATHEMATICS AND OF ARTIFICIAL INTELLIGENCE. - ISSN 1012-2443. - STAMPA. - 34:1-3(2002), pp. 5-34. [10.1023/a:1014422615720]
Probabilistic reasoning under coherence in System P
GILIO, ANGELO
2002
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.