On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems

In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science. Cham: pp. 177-194 (2020)
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Abstract

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated labelled calculus.

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Tim Lyon
Technische Universität Dresden

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References found in this work

The method of hypersequents in the proof theory of propositional non-classical logics.Arnon Avron - 1977 - In Wilfrid Hodges (ed.), Logic. New York: Penguin Books. pp. 1-32.
Proof analysis in intermediate logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1):71-92.
Cut-free sequent calculi for some tense logics.Ryo Kashima - 1994 - Studia Logica 53 (1):119 - 135.
Prefixed tableaus and nested sequents.Melvin Fitting - 2012 - Annals of Pure and Applied Logic 163 (3):291 - 313.

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