Probability Propagation in Generalized Inference Forms

Christian Wallmann, Gernot D. Kleiter

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

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) = α and P(B{pipe}A) = β to P(B) ∈ [αβ, αβ+1-α]. We study generalized inference forms with three or more premises. The generalized Modus Ponens, for example, leads from P(A1) = α1,..., P(An) = αn and P(B{pipe}A1∧·∨An) = β 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 Adam's 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.

Original languageEnglish
Pages (from-to)913-929
Number of pages17
JournalStudia Logica
Volume102
Issue number4
DOIs
Publication statusPublished - Aug 2014

Keywords

  • Coherence
  • Degradation
  • Generalized inference forms
  • Probability logic
  • Probability preservation

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