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Logicality, double-line rules, and modalities. (English) Zbl 07055413

Summary: This paper deals with the question of the logicality of modal logics from a proof-theoretic perspective. It is argued that if Došen’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 Došen’s analysis, allows us to claim that the corresponding modal operators are logical constants.

MSC:

03B45 Modal logic (including the logic of norms)
03F03 Proof theory in general (including proof-theoretic semantics)

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