Labeled Sequent Calculus and Countermodel Construction for Justification Logics

Justification logics are modal-like logics that provide a framework for reasoning about epistemic justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the method due to Sara Negri, we internalize the Kripke-style semantics of justification logics, known as Fitting models, within the syntax of the sequent calculus to produce labeled sequent calculus. We show that our labeled sequent calculi enjoy a weak subformula property, all of the rules are invertible and the structural rules (weakening and contraction) and cut are admissible. Finally soundness and completeness are established, and termination of proof search for some of the labeled systems are shown. We describe a procedure, for some of the labled systems, which produces a derivation for valid sequents and a countermodel for non-valid sequents. We also show a frame correspondence for justification logics in the context of labeled sequent calculus.