Abstract

We study approximate reasoning about continuous-state labeled Markov processes. We show how to approximate a labeled Markov process by a family of finite-state labeled Markov chains. We show that the collection of labeled Markov processes carries a Polish space structure with a countable basis given by finite state Markov chains with rational probabilities. The primary technical tools that we develop to reach these results are A finite-model theorem for the modal logic used to characterize bisimulation A categorical equivalence between the category of Markov processes (with simulation morphisms) with the !-continuous dcpo Proc, defined as the solution of the recursive domain equation Proc = Q Labels P Prob (Proc) 1 . The correspondence between labeled Markov processes and Proc yields a logic complete for reasoning about simulation for continuous-state processes. 1. Introduction Markov processes with continuous state spaces or continuous time evolutions (or both) arise natur...

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