Archive for Mathematical Logic

, Volume 46, Issue 2, pp 73–92

Complexity of admissible rules


DOI: 10.1007/s00153-006-0028-9

Cite this article as:
Jeřábek, E. Arch. Math. Logic (2007) 46: 73. doi:10.1007/s00153-006-0028-9


We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.


Admissible rules Computational complexity Modal logics Intermediate logics 

Mathematics Subject Classification (2000)

03B45 03B55 03D15 

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematical Institute of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic

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