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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.
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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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

[1] Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting. Kluwer, Dordrecht 2002. | MR | Zbl

[2] Finetti, B. De: Theory of Probability. A Critical Introductory Treatment. Volume 1. Wiley, New York 1974. | MR | Zbl

[3] Fréchet, M.: Généralisations du théorème des probabilités totales. Fund. Math. 255 (1935), 379-387. | Zbl

[4] Gilio, A.: Generalization of inference rules in coherence-based probabilistic default reasoning. Internat. J. Approx. Reason. 53 (2012), 413-434. | DOI | MR

[5] Gilio, A., Sanfilippo, G.: Conditional random quantities and iterated conditioning in the setting of coherence. In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty (L. van der Gaag, ed.), Lecture Notes in Comput. Sci. 7958, Springer (2013), pp. 218-229. | MR

[6] Good, I. J.: On the principle of total evidence. British J. Philos. Sci. 17 (1967), 319-321. | DOI

[7] Kleiter, G. D.: Ockham's razor in probability logic. In: Synergies of Soft Computing and Statistics for Intelligent Data Analysis (R. Kruse, M. R. Berthold, C. Moewes, M. A. Gil, P. Grzegorzewski and O. Hryniewicz, eds.). Adv. in Intelligent Systems and Computation 190, Springer (2012), pp. 409-417.

[8] Kyburg, H. E., Teng, C. M.: Uncertain Inference. Cambridge University Press, Cambridge 2001. | MR | Zbl

[9] Lad, F.: Operational Subjective Statistical Methods. Wiley, New York 1996. | MR | Zbl

[10] Manktelow, K. I., Over, D. E., Elqayam, S.: The Science of Reasoning. A Festschrift for Jonathan St B.T. Evans. Psychology Press, New York 2011.

[11] Wagner, C. G.: Modus tollens probabilized. British J. Philos. Sci. 55 (2004), 4, 747-753. | DOI | MR | Zbl

[12] Wallmann, C., Kleiter, G. D.: Exchangeability in probability logic. In: IPMU 2012, Part IV (S. Greco et al., eds.), CCIS 300 (2012), pp. 157-167. | Zbl

[13] Wallmann, C., Kleiter, G. D.: Probability propagation in generalized inference forms. Studia Logica. In press. doi: 10.1007/s11225-013-9513-4. | DOI

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