Skip to main content
Log in

All finitely axiomatizable subframe logics containing the provability logic CSM\(_{0}\) are decidable

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract.

In this paper we investigate those extensions of the bimodal provability logic \({\vec CSM}_{0}\) (alias \({\vec PRL}_{1}\) or \({\vec F}^{-})\) which are subframe logics, i.e. whose general frames are closed under a certain type of substructures. Most bimodal provability logics are in this class. The main result states that all finitely axiomatizable subframe logics containing \({\vec CSM}_{0}\) are decidable. We note that, as a rule, interesting systems in this class do not have the finite model property and are not even complete with respect to Kripke semantics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received July 15, 1997

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wolter, F. All finitely axiomatizable subframe logics containing the provability logic CSM\(_{0}\) are decidable. Arch Math Logic 37, 167–182 (1998). https://doi.org/10.1007/s001530050090

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s001530050090

Navigation