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arXiv · 2309.00486

A new calculus for intuitionistic Strong L\"ob logic: strong termination and cut-elimination, formalised

Ian Shillito·Iris van der Giessen·Rajeev Goré·Rosalie Iemhoff
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Abstract

We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly terminating backward proof search for the intuitionistic Strong L\"ob logic $\sf{iSL}$, an intuitionistic modal logic with a provability interpretation. A novel measure on sequents is used to prove both the termination of the naive backward proof search strategy, and the admissibility of cut in a syntactic and direct way, leading to a straightforward cut-elimination procedure. All proofs have been formalised in the interactive theorem prover Coq.

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Ian Shillito, Iris van der Giessen, Rajeev Goré, Rosalie Iemhoff. 2023-09-01. A new calculus for intuitionistic Strong L\"ob logic: strong termination and cut-elimination, formalised. https://arxiv.org/abs/2309.00486

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