Coalgebraic Modal Logic for Dynamic Systems with Uncertainty

In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures, finitely additive probability measures, plausibilty measures (and their duals, belief functions), and possibility measures. We give axioms and inference rules for the associated system of coalgebraic modal logic, and construct the canonical coalgebras to prove a completeness result.