In multiagent systems, agents usually do not have complete information of the whole system, which makes the analysis of such systems hard. The incompleteness of information is normally modelled by means of accessibility relations, and the schedulers consistent with such relations are called uniform. In this paper, we consider probabilistic multiagent systems with accessibility relations and focus on the model checking problem with respect to the probabilistic epistemic temporal logic, which can specify both temporal and epistemic properties. However, the problem is undecidable in general. We show that it becomes decidable when restricted to memoryless uniform schedulers. Then, we present two algorithms for this case: one reduces the model checking problem into a mixed integer non-linear programming (MINLP) problem, which can then be solved by Satisfiability Modulo Theories (SMT) solvers, and the other is an approximate algorithm based on the upper confidence bounds applied to trees (UCT) algorithm, which can return a result whenever queried. These algorithms have been implemented in an existing model checker and then validated on experiments. The experimental results show the efficiency and extendability of these algorithms, and the algorithm based on UCT outperforms the one based on MINLP in most cases.

在多智能体系统中，智能体通常不具有整个系统的完整信息，这使得对此类系统的分析变得困难。信息的不完整性通常通过可达性关系来建模，符合这种关系的调度器称为统一调度器。在本文中，我们考虑具有可达性关系的概率多智能体系统，并重点关注与概率认知时间逻辑有关的模型检查问题，该逻辑可以指定时间属性和认知属性。然而，这个问题一般来说是无法判定的。我们证明，当限制为无记忆统一调度程序时，它变得可判定。然后，我们针对这种情况提出两种算法：一种将模型检查问题简化为混合整数非线性规划（MINLP）问题，然后可以通过可满足性模理论（SMT）求解器来求解，另一种是近似算法基于应用于树的置信上限 (UCT) 算法，该算法可以在每次查询时返回结果。这些算法已在现有模型检查器中实现，然后通过实验进行验证。实验结果表明了这些算法的高效性和可扩展性，并且在大多数情况下基于UCT的算法优于基于MINLP的算法。