Mechanising a Proof of Craig's Interpolation Theorem for Intuitionistic Logic in Nominal Isabelle

Authors:
Peter Chapman;James Mckinna;Christian Urban
Affiliations:
School of Computer Science, University of St Andrews, Scotland;Department of Computing Science, Radboud University, Nijmegen, Netherlands;Institute for Computer Science, Technical University of Munich, Germany
Venue:
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Year:
2008

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Abstract

Craig's Interpolation Theorem is an important meta- theoretical result for several logics. Here we describe a formalisation of the result for first-order intuitionistic logic without function symbols or equality, with the intention of giving insight into how other such results in proof theory might be mechanically verified, notable cut-admissibility. We use the package Nominal Isabelle, which easily deals with the binding issues in the quantifier cases of the proof.