Authors: Radu Mardare ; Luca Cardelli ; Kim G. Larsen

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".

• 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.)