A decision procedure and complete axiomatization for projection temporal logic

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.