We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the way to developing theories of approximate reasoning for probabilistic systems.
Electronic Notes in Theoretical Computer Science, 2014, p. 211-227
Mathematical Foundations of Programming Semantics, 2014