Probabilistic Alternating-Time <em>µ</em>-Calculus

  • Fu Song ShanghaiTech University
  • Yedi Zhang ShanghaiTech University
  • Taolue Chen Birkbeck, University of London
  • Yu Tang East China Normal University
  • Zhiwu Xu Shenzhen University

Abstract

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.

Published
2019-07-17