A Labeled Deduction System for the Logic UB

We propose an approach for defining labeled natural deduction systems for the class of Peircean branching temporal logics, seen as logics in their own right rather than as sub logics of Ockhamist systems. In particular, we give a system for the logic UB, i.e., the until-free fragment of CTL, and show that it is sound and complete. We also study normalization and discuss how derivations may reduce to a normal form using an appropriate management of proof contexts. Finally, we briefly discuss how to extend our system in order to capture full CTL.