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Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. ... The logic BN4 was defined by R.T. Brady as a four-valued extension of Routley and Meyer's basic logic B. ... Sincere thanks are due to four anonymous referees for their comments on a previous version of this paper. ...doi:10.12775/llp.2021.010 fatcat:zrzfijwqejcq3f3po6zewuwwd4