A First-Order Logic for Reasoning About Higher-Order Upper and Lower Probabilities

  • Nenad Savić
  • Dragan Doder
  • Zoran Ognjanović
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)


We present a first-order probabilistic logic for reasoning about the uncertainty of events modeled by sets of probability measures. In our language, we have formulas that essentially say that “according to agent Ag, for all x, formula \(\alpha (x)\) holds with the lower probability at least \(\frac{1}{3}\)”. Also, the language is powerful enough to allow reasoning about higher order upper and lower probabilities. We provide corresponding Kripke-style semantics, axiomatize the logic and prove that the axiomatization is sound and strongly complete (every satisfiable set of formulas is consistent).


Probabilistic logic Uncertainty Axiomatization Strong completeness 



This work was supported by the SNSF project 200021\(\_\)165549 Justifications and non-classical reasoning, and by the Serbian Ministry of Education and Science through projects ON174026, III44006 and ON174008.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of BernBernSwitzerland
  2. 2.Faculty of Mechanical EngineeringBelgradeSerbia
  3. 3.Mathematical Institute of SASABelgradeSerbia

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