@inproceedings{ISIPTA2023,
author = {Esther Anna Corsi and Tommaso Flaminio and Llu\'is Godo and Hykel Hosni},
title = {A modal logic for uncertainty: a completeness theorem},
booktitle = {13th International Symposium on Imprecise Probabilities: Theories and Applications - ISIPTA 2023},
abstract = {In the present paper, we axiomatize a logic that allows a general approach for reasoning about probability functions, belief functions, lower probabilities and their corresponding duals. The formal setting we consider arises from combining a modalĀ
S5 necessity operator $\Box$ that applies to the formulas of the infinite-valued {\L}ukasiewicz logic with the unary modality P that describes the behaviour of probability functions. The modality P together with an S5 modality $\Box$ provides a language rich enough to characterise probability, belief and lower probability theories. For this logic, we provide an axiomatization and we prove that, once we restrict to suitable sublanguages, it turns out to be sound and complete with respect to belief functions and lower probability models.},
series = {Proceedings of Machine Learning Research},
number = {215},
pages = {119-129},
year = {2023}
}