To specify and verify the concurrent and reactive systems with the theorem proving approach, a complete axiomatization is formalized for first order projection temporal logic (PTL) with both finite and infinite time. To this end, PTL is restricted to a finite domain, and the syntax, semantics as well as the axiomatization of PTL are presented. Further, the techniques of labeled normal form and labeled normal form graph of PTL formulas are introduced respectively, with which a decision procedure for quantifier free PTL (QFPTL) formulas is given. Moreover, a generalized labeled normal form graph is defined and employed to transform a quantified PTL formula into its equivalent QFPTL formula. Finally, a decision procedure for PTL is formalized and the completeness of the axiomatic system is proved based on the decidability of PTL formulas.

为了用定理证明方法指定并验证并发系统和反应系统，对一阶投影时间逻辑（PTL）的有限时间和无限时间进行了完整的公理化。为此，将PTL限制在有限域内，并介绍了PTL的语法，语义以及公理化。此外，分别介绍了PTL公式的标记正态图和标记正态图的技术，并给出了无量词PTL（QFPTL）公式的决策程序。此外，定义了通用的标记正态图，并将其用于将量化的PTL公式转换为其等效的QFPTL公式。最后，确定了PTL的决策程序，并根据PTL公式的可判定性证明了公理系统的完整性。