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Machine-Checked Interpolation Theorems for Substructural Logics Using Display Calculi

  • Jeremy E. DawsonEmail author
  • James Brotherston
  • Rajeev Goré
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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).

Keywords

Craig interpolation Display logic Interactive theorem proving 

Notes

Acknowledgements

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

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jeremy E. Dawson
    • 1
    Email author
  • James Brotherston
    • 2
  • Rajeev Goré
    • 1
  1. 1.Research School of Computer ScienceAustralian National UniversityCanberraAustralia
  2. 2.University College LondonLondonUK

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