Tractable Transformations from Modal Provability Logics into First-Order Logic

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

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

We define a class of modal logics LF by uniformly extending a class of modal logics L. Each logic L is characterised by a class of first-order definable frames, but the corresponding logic LF is sometimes characterised by classes of modal frames that are not first-order definable. The class LF includes provability logics with deep arithmetical interpretations. Using Belnap's proof-theoretical framework Display Logic we characterise the "pseudo-displayable" subclass of LF and show how to define polynomial-time transformations from each such LF into the corresponding L, and hence into first-order classical logic. Theorem provers for classical first-order logic can then be used to mechanise deduction in these pseudo-displayable second order" modal logics.

Mots clés: display logic; modal logic; first-order logic; translation; proof; automated deduction; provability logic

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

Stéphane Demri, Rajeev Goré. Tractable Transformations from Modal Provability Logics into First-Order Logic. 16th International Conference on Automated Deduction Trento, Italy, Harald Ganzinger, Jul 1999, Trento, Italy. pp.16-30, ⟨10.1007/3-540-48660-7_2⟩. ⟨hal-03201407⟩