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Logicality, Double-Line Rules, and Modalities

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Abstract

This paper deals with the question of the logicality of modal logics from a proof-theoretic perspective. It is argued that if Dos̆en’s analysis of logical constants as punctuation marks is embraced, it is possible to show that all the modalities in the cube of normal modal logics are indeed logical constants. It will be proved that the display calculus for each displayable modality admits a purely structural presentation based on double-line rules which, following Dos̆en’s analysis, allows us to claim that the corresponding modal operators are logical constants.

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Acknowledgements

Thanks are due to two anonymous referees and to the audience at the 7th Conference on Non-Classical Logic in Toruń and at the conference General Proof Theory in Tübingen.

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Authors and Affiliations

  1. Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität, Ludwigstr. 31, 80539, München, Germany

    Norbert Gratzl

  2. Dipartimento di Filosofia e Comunicazione, Università di Bologna, Via Zamboni 38, 40126, Bologna, Italy

    Eugenio Orlandelli

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  1. Norbert Gratzl
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  2. Eugenio Orlandelli
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Correspondence to Eugenio Orlandelli.

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Gratzl, N., Orlandelli, E. Logicality, Double-Line Rules, and Modalities. Stud Logica 107, 85–107 (2019). https://doi.org/10.1007/s11225-017-9778-0

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