Probabilistic Modal Logics

Abstract

In this paper probabilistic modal logics that were proposed in the literature will be compared. They will be compared with respect to the purpose they serve, their quantitative or qualitative nature, how their models are constructed and how their axioms behave. The logics will then be classified in a 2x2-matrix which is universal for probabilistic modal logics common in the literature. The distinctions made in the matrix are a quantitative-qualitative one and a distinction between degrees of belief and knowledge about statistical information. It would seem that this matrix signals insurmountable gaps between the varying logics. It will be shown that despite those gaps logics that can bridge the gaps are also possible.