Transitive Reasoning with Imprecise Probabilities

  • Angelo Gilio
  • Niki Pfeifer
  • Giuseppe Sanfilippo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9161)


We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent \(\text{ p-consistent }\) sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.


Coherence Default Imprecise probability Knowledge base P-consistency P-entailment Reasoning Syllogism Weak transitivity 



We thank two anonymous referees for their very useful comments and suggestions.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Angelo Gilio
    • 1
  • Niki Pfeifer
    • 2
  • Giuseppe Sanfilippo
    • 3
  1. 1.Department SBAIUniversity of Rome “La Sapienza” RomeItaly
  2. 2.Munich Center for Mathematical PhilosophyLMU MunichMünchenGermany
  3. 3.Department of Mathematics and Computer ScienceUniversity of PalermoPalermoItaly

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