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Proof Search in Nested Sequent Calculi

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9450))

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Abstract

We propose a notion of focusing for nested sequent calculi for modal logics which brings down the complexity of proof search to that of the corresponding sequent calculi. The resulting systems are amenable to specifications in linear logic. Examples include modal logic \(\mathsf {K}\), a simply dependent bimodal logic and the standard non-normal modal logics. As byproduct we obtain the first nested sequent calculi for the considered non-normal modal logics.

B. Lellmann—Funded by the EU under Marie Skłodowska-Curie grant agreement No. 660047.

E. Pimentel—Funded by CNPq.

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Author information

Authors and Affiliations

  1. Institute of Computer Languages, TU Wien, Vienna, Austria

    Björn Lellmann

  2. Departamento de Matemática, UFRN, Natal, Brazil

    Elaine Pimentel

Authors
  1. Björn Lellmann
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  2. Elaine Pimentel
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Corresponding author

Correspondence to Björn Lellmann .

Editor information

Editors and Affiliations

  1. New York University, New York, New York, USA

    Martin Davis

  2. University of the South Pacific, Suva, Fiji

    Ansgar Fehnker

  3. Macquarie University, Sydney, New South Wales, Australia

    Annabelle McIver

  4. The University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

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Lellmann, B., Pimentel, E. (2015). Proof Search in Nested Sequent Calculi. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2015. Lecture Notes in Computer Science(), vol 9450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48899-7_39

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  • DOI: https://doi.org/10.1007/978-3-662-48899-7_39

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  • Online ISBN: 978-3-662-48899-7

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