Concerning the Semantic Consequence Relation in First-Order Temporal Logic
Article in journal (Refereed)
Theoretical Computer Science(ISSN 0304-3975)
Engineering and Technology
First-order temporal logic; semantic consequence; syntactic consequence; model; completeness; soundness; proof system
In this paper we consider the first-order temporal logic with linear and discrete time. We prove that the set of tautologies of this logic is not arithmetical (i.e., it is neither Σ0n nor Π0n for any natural number n). Thus we show that there is no finitistic and complete axiomatization of the considered logic.