An approach to infinitary temporal proof theory

We investigate from a proof-theoretic viewpoint a propositional and a predicate sequent calculus with an ω–type schema of inference that naturally interpret the propositional and the predicate until –free fragments of Linear Time Logic LTL respectively. The two calculi are based on a natural extension of ordinary sequents and of standard modal rules. We examine the pure propositional case (no extralogical axioms), the propositional and the first order predicate cases (both with a possibly infinite set of extralog- ical axioms). For each system we provide a syntactic proof of cut elimination and a proof of completeness.