Abstract.
The decision problem for provability logic remains PSPACE-complete even if the number of propositional atoms is restricted to one.
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References
Boolos, G.: The Logic of Provability. Cambridge University Press, 1993
Chagrov, A., Rybakov, M.: Least number of variables for PSPACE-hardness of provability problem in systems of modal logic. In: Advances in Modal Logics (AIML’2002). Toulouse, France, Oct. 2002
Hemaspaandra, E.: The complexity of poor man’s logic. J. Logic Comput. 11(4), 609–622 (2001)
Ladner, R.: The computational complexity of provability in systems of modal logic. 6(3), 467–480 (1977)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, 1994
Smoryński, C.: Self-Reference and Modal Logic. Springer, New-York, 1985
Solovay, R.M.: Provability interpretations of modal logic. Israel J. Math. 25, 287–304 (1976)
Spaan, E.: Complexity of Modal Logics. Dissertation, Faculty of Mathematics and Informatics, University of Amsterdam, Amsterdam, 1993
Švejdar, V.: On provability logic. Nordic J. Philosophical Logic 4(2), 95–116 (2000)
Švejdar, V.: On the Polynomial-Space Completeness of Intuitionistic Propositional Logic. Arch. Math. Logic 42, 711–716 (2003)
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This paper was supported by grant 401/01/0218 of the Grant Agency of the Czech Republic.
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Švejdar, V. The decision problem of provability logic with only one atom. Arch. Math. Logic 42, 763–768 (2003). https://doi.org/10.1007/s00153-003-0180-4
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DOI: https://doi.org/10.1007/s00153-003-0180-4