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Titel
Probability propagation in generalized inference forms
VerfasserWallmann, Christian ; Kleiter, Gernot D.
Erschienen in
Studia Logica, Amsterdam, 2014, Jg. 102, H. 4, S. 913-929
ErschienenSpringer Netherlands, 2014
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)Probability logic / Generalized inference forms / Degradation / Probability preservation / Coherence
ISSN1572-8730
URNurn:nbn:at:at-ubs:3-5468 Persistent Identifier (URN)
DOI10.1007/s11225-013-9513-4 
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Probabilistic inference forms lead from point probabilities of the premises to interval probabilities of the conclusion. The probabilistic version of Modus Ponens, for example, licenses the inference from P(A)= and P(B|A)= to P(B)[,+1] . We study generalized inference forms with three or more premises. The generalized Modus Ponens, for example, leads from P(A1)=1,,P(An)=n and P(B|A1An)= to an according interval for P(B). We present the probability intervals for the conclusions of the generalized versions of Cut, Cautious Monotonicity, Modus Tollens, Bayes Theorem, and some SYSTEM O rules. Recently, Gilio has shown that generalized inference forms “degrade”more premises lead to less precise conclusions, i.e., to wider probability intervals of the conclusion. We also study Adams probability preservation properties in generalized inference forms. Special attention is devoted to zero probabilities of the conditioning events. These zero probabilities often lead to different intervals in the coherence and the Kolmogorov approach.