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

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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.

BibTeX - Entry

@InProceedings{cardelli_et_al:LIPIcs:2011:3228,
  author =	{Luca Cardelli and Kim G. Larsen and Radu Mardare},
  title =	{{Continuous Markovian Logic - From Complete Axiomatization to the Metric Space of Formulas}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{144--158},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Marc Bezem},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3228},
  URN =		{urn:nbn:de:0030-drops-32281},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CSL.2011.144},
  annote =	{Keywords: probabilistic logic, axiomatization, Markov processes, metric semantics}
}

Keywords: probabilistic logic, axiomatization, Markov processes, metric semantics
Seminar: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL
Issue date: 2011
Date of publication: 2011


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