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Verification and Refutation of Probabilistic Specifications via Games Kattenbelt, Mark Huth, Michael Probabilistic model checking Markov decision processes Abstraction preorder Stochastic two-player games We develop an abstraction-based framework to check probabilistic specifications of Markov Decision Processes (MDPs) using the stochastic two-player game abstractions (\ie ``games'') developed by Kwiatkowska et al.\ as a foundation. We define an abstraction preorder for these game abstractions which enables us to identify many new game abstractions for each MDP --- ranging from compact and imprecise to complex and precise. This added ability to trade precision for efficiency is crucial for scalable software model checking, as precise abstractions are expensive to construct in practice. Furthermore, we develop a four-valued probabilistic computation tree logic (PCTL) semantics for game abstractions. Together, the preorder and PCTL semantics comprise a powerful verification and refutation framework for arbitrary PCTL properties of MDPs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mark Kattenbelt and Michael Huth 2009 Is Part Of LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2009.2323 urn:nbn:de:0030-drops-23233 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2323 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode