Generalized Probabilistic Modus Ponens

  • Giuseppe SanfilippoEmail author
  • Niki Pfeifer
  • Angelo Gilio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)


Modus ponens (from A and “if A then C” infer C) is one of the most basic inference rules. The probabilistic modus ponens allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P(A) and P(C|A) infer P(C)). In this paper, we generalize the probabilistic modus ponens by replacing A by the conditional event A|H. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the conclusion. Interestingly, the propagation rules for the lower and the upper bounds on the conclusion of the generalized probabilistic modus ponens coincide with the respective bounds on the conclusion for the (non-nested) probabilistic modus ponens.


Coherence Conditional random quantities Conjoined conditionals Iterated conditionals Modus ponens Prevision 



We thank three anonymous referees for their useful comments and suggestions. We thank DFG, FMSH, and Villa Vigoni for supporting joint meetings at Villa Vigoni where parts of this work originated (Project: “Human Rationality: Probabilistic Points of View”).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

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