Quantitative Model Checking of Knowledge

Model checking, a formal and automatic verification method, has been widely used to check specifications expressed not only as qualitative properties (e.g safety and liveliness), but also as quantitative properties (e.g. degree of reliability and reachability). In this paper, we present a method for probabilistic model checking of multi-agent systems specified by a probabilistic-epistemic logic PCTLK. We define transformations from probabilistic interpreted systems into Discrete-time Markov chains(DTMC) and from PCTLK formulae to PCTL formulae so that we are able to convert PCTLK model checking problems into PCTL model checking problem. The algorithm is implemented in the probabilistic model checker PRISM. Some properties, including agents’ probabilistic knowledge, are verified and simulations are shown.

[1]  R. Durrett.  Probability: Theory and Examples , 1993 .

[2]  Wojciech Jamroga.  A temporal logic for Markov chains , 2008, AAMAS.

[3]  Christel Baier,et al.  Principles of model checking , 2008 .

[4]  Jacques Wainer,et al.  Modeling Action, Knowledge and Control , 1998, ECAI.

[5]  Alessio Lomuscio,et al.  A Complete First-Order Logic of Knowledge and Time , 2008, KR.

[6]  Wojciech Penczek,et al.  Symbolic model checking for temporal-epistemic logics , 2007, SIGA.

[7]  Mario R. F. Benevides,et al.  Verification of Epistemic Properties in Probabilistic Multi-Agent Systems , 2009, MATES.

[8]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[9]  Marta Z. Kwiatkowska,et al.  Probabilistic symbolic model checking with PRISM: a hybrid approach , 2004, International Journal on Software Tools for Technology Transfer.

[10]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[11]  Leslie Pack Kaelbling,et al.  Planning and Acting in Partially Observable Stochastic Domains , 1998, Artif. Intell..

[12]  Jamal Bentahar,et al.  Model Checking Epistemic and Probabilistic Properties of Multi-agent Systems , 2011, IEA/AIE.

[13]  Wojciech Penczek,et al.  Verifying epistemic properties of multi-agent systems via bounded model checking , 2002, AAMAS '03.

[14]  Alessio Lomuscio,et al.  Quantified epistemic logics for reasoning about knowledge in multi-agent systems , 2009, Artif. Intell..

[15]  Marta Z. Kwiatkowska,et al.  PRISM: Probabilistic Symbolic Model Checker , 2002, Computer Performance Evaluation / TOOLS.

[16]  Leslie Pack Kaelbling,et al.  Partially Observable Markov Decision Processes for Artificial Intelligence , 1995, KI.

[17]  Alessio Lomuscio,et al.  Automatic Verification of Knowledge and Time with NuSMV , 2007, IJCAI.

[18]  Cheng Luo,et al.  Symbolic model checking of probabilistic knowledge , 2011, TARK XIII.

[19]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[20]  Leslie Pack Kaelbling,et al.  Acting Optimally in Partially Observable Stochastic Domains , 1994, AAAI.