Probabilistic Alternating-Time µ -Calculus

Reasoning about strategic abilities is key to an AI system consisting of multiple agents with random behaviors. We propose a probabilistic extension of Alternating µ-Calculus (AMC), named PAMC, for reasoning about strategic abilities of agents in stochastic multi-agent systems. PAMC subsumes existing logics AMC and PµTL. The usefulness of PAMC is exemplified by applications in genetic regulatory networks. We show that, for PAMC, the model checking problem is in UP∩co-UP, and the satisfiability problem is EXPTIME-complete, both of which are the same as those for AMC. Moreover, PAMC admits the small model property. We implement the satisfiability checking procedure in a tool PAMCSolver.

Authors

• Fu Song Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China Nanjing Institute of Software Technology, Nanjing, China
• Yedi Zhang National University of Singapore, Singapore
• Taolue Chen
• Yu Tang
• Zhiwu Xu

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