Machine-Checked Interpolation Theorems for Substructural Logics Using Display Calculi
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).
KeywordsCraig interpolation Display logic Interactive theorem proving
We are grateful for the many comments from the IJCAR reviewers, which have improved the paper considerably.
- 1.Isabelle/HOL mechanisation of our interpolation proofs. http://users.cecs.anu.edu.au/ jeremy/isabelle/2005/interp/
- 4.Buss, S.R.: Introduction to proof theory. In: Handbook of Proof Theory, chap. I. Elsevier Science (1998)Google Scholar