A Unified Gentzen-style Framework for Until-free LTL

Abstract

A unified Gentzen-style framework for until-free propositional linear-time temporal logic is introduced. The proposed framework, based on infinitary rules and rules for primitive negation, can handle uniformly both a single-succedent sequent calculus and a natural deduction system. Furthermore, an equivalence between these systems, alongside with proofs of cut-elimination and normalization theorems, is established.