A Labelled Sequent-Calculus for Observation Logic

We investigate observation logic, an intuitionnistic modal logic designed for reasoning about approximation and multiple contexts, and propose a sequent-calculus formulation of this logic. Due to the validy of an axiom (called T2) which is a weakening of T, one needs an adaptation of the usual sequent-calculus formalism in order to have some classical properties of sequent calculus, such as cut elimination and the subformula property. To solve this problem, we propose to assign to each proposition inside a proof a label, carrying some context information, and show the validity of some expected properties and manipulations in this framework.