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

Christian Wallmann, Gernot Kleiter

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)268-283
Number of pages16
JournalKybernetika
Volume50
Issue number2
DOIs
Publication statusPublished - Mar 2014

Keywords

  • Coherence
  • Degradation
  • Generalized inference forms
  • Probabilistic modus tollens
  • Probability logic
  • Total evidence

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