Archive for Mathematical Logic

, Volume 46, Issue 2, pp 73–92 | Cite as

Complexity of admissible rules

  • Emil Jeřábek


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 


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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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