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

Gratzl, N., Orlandelli, E. (2018). Logicality, Double-Line Rules, and Modalities. STUDIA LOGICA, online first, 1-23 [10.1007/s11225-017-9778-0].

Logicality, Double-Line Rules, and Modalities

Orlandelli, Eugenio
2018

Abstract

This paper deals with the question of the logicality of modal logics from a proof-theoretic perspective. It is argued that if Do˘sen’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 Do˘sen’s analysis, allows us to claim that the corresponding modal operators are logical constants.
2018
Gratzl, N., Orlandelli, E. (2018). Logicality, Double-Line Rules, and Modalities. STUDIA LOGICA, online first, 1-23 [10.1007/s11225-017-9778-0].
Gratzl, Norbert; Orlandelli, Eugenio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/618394
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