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An application of Rieger-Nishimura formulas to the intuitionistic modal logics

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Abstract

The main results of the paper are the following: For each monadic prepositional formula φ which is classically true but not intuitionistically so, there is a continuum of intuitionistic monotone modal logics L such that L+φ is inconsistent.

There exists a consistent intuitionistic monotone modal logic L such that for any formula φ of the kind mentioned above the logic L+φ is inconsistent.

There exist at least countably many maximal intuitionistic monotone modal logics.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Dimiter Vakarelov

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  1. Dimiter Vakarelov
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The author appreciates very much referees' suggestions which helped to improve the exposition.

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Vakarelov, D. An application of Rieger-Nishimura formulas to the intuitionistic modal logics. Stud Logica 44, 79–85 (1985). https://doi.org/10.1007/BF00370811

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  • DOI: https://doi.org/10.1007/BF00370811

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