Two distinct and apparently "dual" traditions of non-classical logic, three-valued logic and paraconsistent logic, are considered here and a unified presentation of "easy-to-handle" versions of these logics is given, in which full naive set theory, i.e. Frege's comprehension principle + extensionality, is not absurd.
Roland Hinnion. "Naive Set Theory with Extensionality in Partial Logic and in Paradoxical Logic." Notre Dame J. Formal Logic 35 (1) 15 - 40, Winter 1994. https://doi.org/10.1305/ndjfl/1040609292