文章基本信息

标题：Continuous Markovian Logic - From Complete Axiomatization to the Metric Space of Formulas
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作者：Luca Cardelli ; Kim G. Larsen ; Radu Mardare 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2011
卷号：12
页码：144-158
DOI：10.4230/LIPIcs.CSL.2011.144
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：probabilistic logic; axiomatization; Markov processes; metric semantics