Cut-elimination for Weak Grzegorczyk Logic Go

We present a syntactic proof of cut-elimination for weak Grzegorczyk logic Go. The logic has a syntactically similar axiomatisation to Gödel-Löb logic GL (provability logic) and Grzegorczyk's logic Grz. Semantically, GL can be viewed as the irreflexive counterpart of Go, and Grz can be viewed as the reflexive counterpart of Go. Although proofs of syntactic cut-elimination for GL and Grz have appeared in the literature, this is the first proof of syntactic cut-elimination for Go. The proof is technically interesting, requiring a deeper analysis of the derivation structures than the proofs for GL and Grz. New transformations generalising the transformations for GL and Grz are developed here.