The decision problem of provability logic with only one atom

November 2003, Volume 42, Issue 8, pp 763–768 | Cite as

Article

First Online: 13 June 2003

Abstract.

The decision problem for provability logic remains PSPACE-complete even if the number of propositional atoms is restricted to one.

Provability logic Non-classical logics Polynomial-space Kripke models Propositional atoms

This is a preview of subscription content, to check access.

Unable to display preview. Download preview PDF.

1.
Boolos, G.: The Logic of Provability. Cambridge University Press, 1993Google Scholar
2.
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. 2002Google Scholar
3.
Hemaspaandra, E.: The complexity of poor man’s logic. J. Logic Comput. 11(4), 609–622 (2001)zbMATHGoogle Scholar
4.
Ladner, R.: The computational complexity of provability in systems of modal logic. 6(3), 467–480 (1977)Google Scholar
5.
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, 1994Google Scholar
6.
Smoryński, C.: Self-Reference and Modal Logic. Springer, New-York, 1985Google Scholar
7.
Solovay, R.M.: Provability interpretations of modal logic. Israel J. Math. 25, 287–304 (1976)zbMATHGoogle Scholar
8.
Spaan, E.: Complexity of Modal Logics. Dissertation, Faculty of Mathematics and Informatics, University of Amsterdam, Amsterdam, 1993Google Scholar
9.
Švejdar, V.: On provability logic. Nordic J. Philosophical Logic 4(2), 95–116 (2000)Google Scholar
10.
Švejdar, V.: On the Polynomial-Space Completeness of Intuitionistic Propositional Logic. Arch. Math. Logic 42, 711–716 (2003)Google Scholar