Logicality, Double-Line Rules, and Modalities

Studia Logica 107 (1):85-107 (2019)
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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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Citations of this work

Proof-theoretic pluralism.Filippo Ferrari & Eugenio Orlandelli - 2019 - Synthese 198 (Suppl 20):4879-4903.

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References found in this work

What is logic?Ian Hacking - 1979 - Journal of Philosophy 76 (6):285-319.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Display logic.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (4):375-417.
Modal Logic.James W. Garson - 2009 - Stanford Encyclopedia of Philosophy.

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