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

Cardelli, Luca; Larsen, Kim G.; Mardare, Radu

doi:10.4230/LIPIcs.CSL.2011.144

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

Authors Luca Cardelli, Kim G. Larsen, Radu Mardare

Part of: Volume: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (CSL 2011)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computer Science Logic (CSL)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2011-08-31

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Document Identifiers

DOI: 10.4230/LIPIcs.CSL.2011.144
URN: urn:nbn:de:0030-drops-32281

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Keywords

probabilistic logic
axiomatization
Markov processes
metric semantics

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Abstract

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 definition of a quantified extension of satisfiability relation that measures the compatibility of a model and a property. Relying on the small model property, we prove that this measure can be approximated, within a given error, by using a distance between logical formulas.

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Luca Cardelli, Kim G. Larsen, and Radu Mardare. Continuous Markovian Logic - From Complete Axiomatization to the Metric Space of Formulas. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 144-158, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011) https://doi.org/10.4230/LIPIcs.CSL.2011.144

Author Details

Luca Cardelli

Kim G. Larsen

Radu Mardare

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