Geodesic
Degradation in probability logic: When more information leads to less precise conclusions
Kybernetika, Tome 50 (2014) no. 2, pp. 268-283.

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Probability logic studies the properties resulting from the probabilistic interpretation of logical argument forms. Typical examples are probabilistic Modus Ponens and Modus Tollens. Argument forms with two premises usually lead from precise probabilities of the premises to imprecise or interval probabilities of the conclusion. In the contribution, we study generalized inference forms having three or more premises. Recently, Gilio has shown that these generalized forms “degrade” – more premises lead to more imprecise conclusions, i. e., to wider intervals. We distinguish different forms of degradation. We analyse Predictive Inference, Modus Ponens, Bayes' Theorem, and Modus Tollens. Special attention is devoted to the case where the conditioning events have zero probabilities. Finally, we discuss the relation of degradation to monotonicity.
DOI : 10.14736/kyb-2014-2-0268
Classification : 03B48, 68T37, 97K50
Keywords: probability logic; generalized inference forms; degradation; total evidence; coherence; probabilistic Modus Tollens 
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     title = {Degradation in probability logic: {When} more information leads to less precise conclusions},
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Wallmann, Christian; Kleiter, Gernot D. Degradation in probability logic: When more information leads to less precise conclusions. Kybernetika, Tome 50 (2014) no. 2, pp. 268-283. doi : 10.14736/kyb-2014-2-0268. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-2-0268/

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