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.
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Received July 15, 1997
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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
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DOI: https://doi.org/10.1007/s001530050090