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In this paper we continue our research line on logical characterizations of behavioral metrics 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.
Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic variant of the
The combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to trace and
This is an attempt to illustrate the glorious history of logical foundations and to discuss the uncertain future.
We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification performance, ro
Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can be reconc