From Display to Labelled Proofs for Tense Logics

In Anil Nerode & Sergei Artemov (eds.), Logical Foundations of Computer Science. Springer International Publishing. pp. 120 - 139 (2018)

Tim Lyon
Vienna University of Technology
We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.
Keywords Display calculus  Labelled calculus  Structural proof theory  Tense logic  Modal logic
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