 As already mentioned, Cantwell’s three-valued connexive logic CN can be obtained by extending MC with the Law of Excluded Middle and, semantically, by requiring that for every propositional variable p and every model M, M ⊨ p or M ⊨ ~p. There is another three-valued connexive logic that is strictly stronger than CN, namely the “dialetheic Logic of Paradox,” dLP, studied in Omori 2016c, which turned out to be equivalent with the system LImp from Olkhovikov 2002 (published in English translation in 2016). Whilst Olkhovikov uses a unary operator L, understood as a kind of necessity operator, in the language of LImp, Omori uses a unary consistency operator, ○, in the language of dLP. The connective L is definable in dLP, and the connective ○ is definable in LImp. It is shown in Omori 2016c that dLP is inconsistent, definitionally complete, and Post complete. Both, Omori (2016c) and Olkhovikov (2016) consider a first-order extension of dLP, respectively LImp.