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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)
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.Author's Profile
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Citations of this work
On the Correspondence between Nested Calculi and Semantic Systems for Intuitionistic Logics.Tim Lyon - 2021 - Journal of Logic and Computation 31 (1):213-265.
Refining Labelled Systems for Modal and Constructive Logics with Applications.Tim Lyon - 2021 - Dissertation, Technischen Universität Wien
References found in this work
The method of hypersequents in the proof theory of propositional non-classical logics.Arnon Avron - 1996 - In Wilfrid Hodges (ed.), Logic: Foundations to Applications. Oxford: pp. 1-32.
Proof analysis in intermediate logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1):71-92.
Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents.Tim Lyon, Alwen Tiu, Rajeev Gore & Ranald Clouston - 2020 - In Maribel Fernandez & Anca Muscholl (eds.), 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Dagstuhl, Germany: pp. 1-16.
Tableau methods of proof for modal logics.Melvin Fitting - 1972 - Notre Dame Journal of Formal Logic 13 (2):237-247.
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