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Title: What is Normal?
Author(s): KUBYSHKINA, Ekaterina , PETROLO, Mattia
Journal: Logique et Analyse
Volume: 257    Date: 2022   
Pages: 25-37
DOI: 10.2143/LEA.257.0.3291069

Abstract :
On the basis of the definition of a normal modal system, it is common to distinguish between normal and non-normal modal operators. However, we argue that the standard definition of a normal operator in the literature leads to at least two problems. First, it induces a mismatch between the normality of a system and the attribution of normality to an operator of this system. Second, the standard definition is insensitive to different occurrences of the possibility operator in various normal and non-normal systems. We introduce a definition of normal operator which is not affected by either of these problems, and discuss its applications both to the monomodal and to the multimodal settings.

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