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On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems

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Logical Foundations of Computer Science (LFCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11972))

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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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Notes

  1. 1.

    Treelike sequents are equivalently characterized as sequents with graphs that are: (i) connected, (ii) acyclic, and (iii) contain no backwards branching.

  2. 2.

    In the propositional setting, these sequents become \(\mathcal {R},w \le v, w : A, \varGamma \Rightarrow v : A, \varDelta \) and \(\mathcal {R}, w:A,\varGamma \Rightarrow \varDelta , w :A\), respectively.

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Acknowledgments

The author would like to express his gratitude to his PhD supervisor A. Ciabattoni for her support and helpful comments. Work funded by FWF projects I2982, Y544-N2, and W1255-N23.

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Authors and Affiliations

  1. Institut für Logic and Computation, Technische Universität Wien, 1040, Vienna, Austria

    Tim Lyon

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  1. Tim Lyon
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Correspondence to Tim Lyon .

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Editors and Affiliations

  1. The Graduate Center, CUNY, New York, NY, USA

    Sergei Artemov

  2. Cornell University, Ithaca, NY, USA

    Anil Nerode

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Lyon, T. (2020). On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2020. Lecture Notes in Computer Science(), vol 11972. Springer, Cham. https://doi.org/10.1007/978-3-030-36755-8_12

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