Logicality, Double-Line Rules, and Modalities
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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.
KeywordsNormal modalities Logicality Double-line rules Proof-theoretic semantics Display calculi
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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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