An O ((n·log n)3)-Time Transformation from Grz into Decidable Fragments of Classical First-Order Logic

@inproceedings{Demri1998AnO,
  title={An O ((n·log n)3)-Time Transformation from Grz into Decidable Fragments of Classical First-Order Logic},
  author={St{\'e}phane Demri and Rajeev Gor{\'e}},
  booktitle={FTP},
  year={1998}
}
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… 
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