Abstract
We consider the well-known provability logic GLP. We prove that the GLP-provability problem for polymodal formulas without variables is PSPACE-complete. For a number n, let \({L^{n}_0}\) denote the class of all polymodal variable-free formulas without modalities \({\langle n \rangle,\langle n+1\rangle,...}\). We show that, for every number n, the GLP-provability problem for formulas from \({L^{n}_0}\) is in PTIME.
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Pakhomov, F. On the complexity of the closed fragment of Japaridze’s provability logic. Arch. Math. Logic 53, 949–967 (2014). https://doi.org/10.1007/s00153-014-0397-4
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DOI: https://doi.org/10.1007/s00153-014-0397-4