Continuous Markovian Logic - From Complete Axiomatization to the Metric Space of Formulas

Luca Cardelli, Kim G. Larsen & Radu Mardare
Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-space and continuous-time labelled Markov processes (CMPs). The modalities of CML approximate the rates of the exponentially distributed random variables that characterize the duration of the labeled transitions. In this paper we present a sound and complete Hilbert-style axiomatization of CML for the CMP-semantics and prove some metaproperties including the small model property. CML characterizes stochastic bisimulation and supports the...