On Paracomplete Versions of Jaśkowskis Discussive Logic

Jaśkowski's discussive (discursive) logic \( \mathbf{D_2} \) is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic \( \mathbf{ S5 } \) via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic \( \mathbf{ D_2^p } \).