 Beside those proposals, Omori (2019) focuses also on the interplay of negation, modals, and conditionals in the framework of connexive logics. Omori uses Odintsov and Wansing’s (2010) four-valued framework for modal logic, to show that conditional negations of varying strength for \(A&gt;B\) can be derived from the outer negation of a conditional (building on distinctions made in Égré &amp; Politzer 2013), in particular \(A&gt;{\Diamond\neg B}\) instead of \(A &gt;\neg B\). He gives sound and complete axiomatizations for the resulting conditional logics. An earlier connexive system is Olkhovikov (2002)’s logic LImp, effectively combining Cooper’s conditional with a trivalent necessity operator of determinate truth (mapping 1 to 1 and ½ and 0 to 0).