We investigate a modal logic for expressing properties of Markov processes whose semantics is real-valued, rather than Boolean, and based on the mathematical theory of Riesz spaces. We use the duality theory of Riesz spaces to provide a connection between Markov processes and the logic. This takes the form of a duality between the category of coalgebras of the Radon monad (modeling Markov processes) and the category of a new class of algebras (algebraizing the logic) which we call modal Riesz spaces. As a result, we obtain a sound and complete axiomatization of the Riesz Modal logic.

This is joint work with Robert Furber and Radu Mardare.