Fragmenting Modal Logic

Fragmentalism allows incompatible facts to constitute reality in an absolute\r\nmanner, provided that they fail to obtain together. In recent years, the view\r\nhas been extensively discussed, with a focus on its formalisation in modeltheoretic\r\nterms. This paper focuses on three formalisations: Lipman’s\r\napproach, the subvaluationist interpretation, and a novel view that has been\r\nso far overlooked. The aim of the paper is to explore the application of these\r\nformalisations to the alethic modal case. This logical exploration will allow us\r\nto study (i) cases of metaphysical incompatibility between modal facts and\r\n(ii) cases of modal dialetheias. In turn, this will enrich our understanding of\r\nthe role of impossibility in the fragmentalist framework.