Abstract
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.
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The research was done while the author was visiting the Department of Philosophy of the Utrecht University. Supported by grant IAA1019401 of GA AV ČR
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Jeřábek, E. Complexity of admissible rules. Arch. Math. Logic 46, 73–92 (2007). https://doi.org/10.1007/s00153-006-0028-9
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DOI: https://doi.org/10.1007/s00153-006-0028-9