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A new calculus for intuitionistic Strong Löb logic: strong termination and cut-elimination, formalised (2309.00486v1)
Published 1 Sep 2023 in cs.LO and math.LO
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.