Degradation in probability logic: When more information leads to less precise conclusions

Wallmann, Christian, and Kleiter, Gernot D.. "Degradation in probability logic: When more information leads to less precise conclusions." Kybernetika 50.2 (2014): 268-283. <http://eudml.org/doc/261862>.

@article{Wallmann2014,
abstract = {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.},
author = {Wallmann, Christian, Kleiter, Gernot D.},
journal = {Kybernetika},
keywords = {probability logic; generalized inference forms; degradation; total evidence; coherence; probabilistic Modus Tollens; probability logic; generalized inference forms; degradation; total evidence; coherence; probabilistic modus tollens},
language = {eng},
number = {2},
pages = {268-283},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Degradation in probability logic: When more information leads to less precise conclusions},
url = {http://eudml.org/doc/261862},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Wallmann, Christian
AU - Kleiter, Gernot D.
TI - Degradation in probability logic: When more information leads to less precise conclusions
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 2
SP - 268
EP - 283
AB - 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.
LA - eng
KW - probability logic; generalized inference forms; degradation; total evidence; coherence; probabilistic Modus Tollens; probability logic; generalized inference forms; degradation; total evidence; coherence; probabilistic modus tollens
UR - http://eudml.org/doc/261862
ER -