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

Stéphane Demri (1, 2, 3) , Rajeev Goré (3)

1 Leibniz - IMAG - Laboratoire Leibniz
2 CNRS - Centre National de la Recherche Scientifique
3 ANU - Australian National University

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 .

Mots clés: modal logic Grz; translation; first-order logic; FO2; sequent-style proof system; complexity

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Stéphane Demri, Rajeev Goré. An O((n.log n) 3 )-time transformation from Grz into decidable fragments of classical first-order logic. International Workshop on First order Theorem Proving (FTP'98), Ricardo Caferra; Gernot Salzer, Nov 1998, Vienna, Austria. pp.153-167. ⟨hal-03195009⟩