摘要：We introduce a novel real-valued endogenous logic for expressing propertiesof probabilistic transition systems called Riesz modal logic. The design of thesyntax and semantics of this logic is directly inspired by the theory of Rieszspaces, a mature field of mathematics at the intersection of universal algebraand functional analysis. By using powerful results from this theory, we developthe duality theory of the Riesz modal logic in the form of analgebra-to-coalgebra correspondence. This has a number of consequencesincluding: a sound and complete axiomatization, the proof that the logiccharacterizes probabilistic bisimulation and other convenient results such ascompletion theorems. This work is intended to be the basis for subsequentresearch on extensions of Riesz modal logic with fixed-point operators.
