Logical Characterization of Trace Metrics

In this paper we continue our research line on logical characterizations of behavioralmetrics obtained from the definition of a metric over the set of logical properties of interest. This time we provide a characterization of both strong and weak trace metric on nondeterministic probabilistic processes, based on a minimal boolean logic L which we prove to be powerful enough to characterize strong and weak probabilistic trace equivalence. Moreover,we also prove that our characterization approach can be restated in terms of a more classic probabilistic L-model checking problem.