Logicality, Double-Line Rules, and Modalities

Gratzl, Norbert and Orlandelli, Eugenio (19. January 2018): Logicality, Double-Line Rules, and Modalities. In: Studia Logica, Vol. 107, No. 1: pp. 85-107

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.

• Item Type: Journal article
• Keywords: Normal modalities, Logicality, Double-line rules, Proof-theoretic semantics, Display calculi
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic
• Subjects: 100 Philosophy and Psychology > 160 Logic
• ISSN: 1572-8730
• Language: English