We study a propositional probabilistic temporal epistemic logic $\textbf {PTEL}$ with both future and past temporal operators, with non-rigid set of agents and the operators for agents’ knowledge and for common knowledge and with probabilities defined on the sets of runs and on the sets of possible worlds. A semantics is given by a class ${\scriptsize{\rm Mod}}$ of Kripke-like models with possible worlds. We prove decidability of $\textbf {PTEL}$ by showing that checking satisfiability of a formula in ${\scriptsize{\rm Mod}}$ is equivalent to checking its satisfiability in a finite set of finitely representable structures. The same procedure can be applied to the class of all synchronous ${\scriptsize{\rm Mod}}$-models. We give an upper complexity bound for the satisfiability problem for ${\scriptsize{\rm Mod}}$.

中文翻译：

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概率时间认知逻辑：可判定性

我们研究一个命题概率时间认知逻辑 $\textbf {PTEL}$ ，它具有未来和过去的时间运算符，具有非刚性的代理集以及代理知识和公共知识的运算符以及在运行集上定义的概率以及可能世界的集合。语义由具有可能世界的类 Kripke 模型的 ${\scriptsize{\rm Mod}}$ 类给出。我们通过证明检查 ${\scriptsize{\rm Mod}}$ 中公式的可满足性相当于检查其在有限可表示结构的有限集合中的可满足性来证明 $\textbf {PTEL}$ 的可判定性。相同的过程可以应用于所有同步 ${\scriptsize{\rm Mod}}$-模型的类。我们给出 ${\scriptsize{\rm Mod}}$ 的可满足性问题的复杂度上限。