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Modality and Paraconsistency

Paraconsistent logic was born in the vicinity of modal logic. Moreover, as every other non-classical logicians, paraconsistentists have very often flirted with modalities. The first known system of paraconsistent logic was in fact defined as a fragment of S5, in the late 40s. But a fragment of a modal system is not necessarily a modal system. I will show here, indeed, that Jaśkowski’s D2 is not a modal logic, in the contemporary usual meaning of the term. By contrast, I will also show, subsequently, that any non-degenerate normal modal system is inherently paraconsistent.