European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty

ECSQARU 2015: Symbolic and Quantitative Approaches to Reasoning with Uncertainty pp 95-105

Transitive Reasoning with Imprecise Probabilities

Conference paper

DOI: 10.1007/978-3-319-20807-7_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9161)
Cite this paper as:
Gilio A., Pfeifer N., Sanfilippo G. (2015) Transitive Reasoning with Imprecise Probabilities. In: Destercke S., Denoeux T. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2015. Lecture Notes in Computer Science, vol 9161. Springer, Cham


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 

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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