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

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)

## Abstract

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).

## Keywords

Probabilistic logic Uncertainty Axiomatization Strong completeness

## Notes

### Acknowledgments

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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