A Complete Axiomatic Characterization of First-Order Temporal Logic of Linear Time
Article in journal (Refereed)
Theoretical Computer Science(ISSN 0304-3975)
Engineering and Technology
Algebra of Lindenbaum and Tarski | Boolean algebra | completeness | consistency | First-Order Temporal Logic | Kripke structure | model | proof system | semantic consequence | soundness | syntactic consequence
As shown in (Szalas, 1986, 1986, 1987) there is no finitistic and complete axiomatization of First-Order Temporal Logic of linear and discrete time. In this paper we give an infinitary proof system for the logic. We prove that the proof system is sound and complete. We also show that any syntactically consistent temporal theory has a model. As a corollary we obtain that the Downward Theorem of Skolem, Lowenheim and Tarski holds in the case of considered logic.