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arXiv · 1211.5190

Continuous Markovian Logics - Axiomatization and Quantified Metatheory

Radu Mardare·Luca Cardelli·Kim G. Larsen
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Abstract

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 allows us to prove two robustness theorems for the logic stating that one can perturb formulas and maintain "approximate satisfaction".

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Radu Mardare, Luca Cardelli, Kim G. Larsen. 2012-11-22. Continuous Markovian Logics - Axiomatization and Quantified Metatheory. https://doi.org/10.2168/lmcs-8(4%3A19)2012

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