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Continuous Markovian logics – axiomatization and quantified metatheory. (English) Zbl 1261.03088

Summary: Continuous Markovian logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic) state-spaces, henceforth called continuous Markov processes (CMPs). The modalities of CML evaluate the rates of the exponentially distributed random variables that characterize the duration of the labeled transitions of a CMP. In this paper we present weak and strong complete axiomatizations for CML and prove a series of metaproperties, including the finite model property and the construction of canonical models. CML characterizes stochastic bisimilarity and it supports the definition of a quantified extension of the satisfiability relation that measures the “compatibility” between a model and a property. In this context, the metaproperties allow us to prove two robustness theorems for the logic stating that one can perturb formulas and maintain “approximate satisfaction”.

MSC:

03B45 Modal logic (including the logic of norms)
60J25 Continuous-time Markov processes on general state spaces
68Q87 Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
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