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International Joint Conference on Automated Reasoning

IJCAR 2016: Automated Reasoning pp 452–468Cite as

Machine-Checked Interpolation Theorems for Substructural Logics Using Display Calculi

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9706))

Abstract

We present a mechanised formalisation, in Isabelle/HOL, of Brotherston and Goré’s proof of Craig interpolation for a large of class display calculi for various propositional substructural logics. Along the way, we discuss the particular difficulties associated with the local interpolation property for various rules, and some important differences between our proofs and those of Brotherston and Goré, which are motivated by the ease of mechanising the development. Finally, we discuss the value for this work of using a prover with a programmable user interface (here, Isabelle with its Standard ML interface).

J.E. Dawson—Supported by Australian Research Council Discovery Grant DP120101244.

J. Brotherston—Supported by an EPSRC Career Acceleration Fellowship.

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Notes

  1. 1.

    In Lemma 3.9 [3] this set of rules is the set of AD rules.

References

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Acknowledgements

We are grateful for the many comments from the IJCAR reviewers, which have improved the paper considerably.

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Authors and Affiliations

  1. Research School of Computer Science, Australian National University, Canberra, Australia

    Jeremy E. Dawson & Rajeev Goré

  2. University College London, London, UK

    James Brotherston

Authors
  1. Jeremy E. Dawson
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  2. James Brotherston
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  3. Rajeev Goré
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Corresponding author

Correspondence to Jeremy E. Dawson .

Editor information

Editors and Affiliations

  1. Aix-Marseille University, Marseille, France

    Nicola Olivetti

  2. SRI International, Menlo Park, California, USA

    Ashish Tiwari

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Dawson, J.E., Brotherston, J., Goré, R. (2016). Machine-Checked Interpolation Theorems for Substructural Logics Using Display Calculi. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_31

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  • DOI: https://doi.org/10.1007/978-3-319-40229-1_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40228-4

  • Online ISBN: 978-3-319-40229-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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