Labeled sequent calculus for justification logics

Annals of Pure and Applied Logic 168 (1):72-111 (2017)
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Abstract

Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for combined modal-justification logics. Using a method due to Sara Negri, we internalize the Kripke-style semantics of justification and modal-justification logics, known as Fitting models, within the syntax of the sequent calculus to produce labeled sequent calculi. We show that all rules of these systems are invertible and the structural rules (weakening and contraction) and the cut rule are admissible. Soundness and completeness are established as well. The analyticity for some of our labeled sequent calculi are shown by proving that they enjoy the subformula, sublabel and subterm properties. We also present an analytic labeled sequent calculus for S4LPN based on Artemov–Fitting models.

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Author's Profile

Meghdad Ghari
University Of Isfahan

References found in this work

Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
The logic of justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
The logic of proofs, semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
Cut Elimination in the Presence of Axioms.Sara Negri & Jan Von Plato - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.

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