An O((n · log n)3)-time transformation from Grz into decidable fragments of classical first-order logic

Abstract

The provability logic Grz is characterized by a class of modal frames that is not first-order definable. We present a simple embedding of Grz into decidable fragments of classical first-order logic such as FO2 and the guarded fragment. The embedding is an O((n.log n)3)-time transformation that neither involves first principles about Turing machines (and therefore is easy to implement), nor the semantical characterization of Grz (and therefore does not use any second-order machinery). Instead, we use the syntactic relationships between cut-free sequent-style calculi for Grz, S4 and T. We first translate Grz into T, and then we use the relational translation from T into FO2. Show more