In this paper we show that, when analyzed with contemporary tools in logic—such as Dunn-style semantics, Reichenbach’s three-valued logic exhibits many interesting features, and even new responses to some of the old objections to it can be attempted. Also, we establish some connections between Reichenbach’s three-valued logic and some contra-classical logics.

In [23], Mortensen introduced a connexive logic commonly known as 'M3V'. M3V is obtained by adding a special conditional to LP. Among its most notable features, besides its being connexive, M3V is negation-inconsistent and it validates the negation of every conditional. But Mortensen has also studied and applied extensively other non-connexive logics, for example, closed set logic, CSL, and a variant of Sette's logic, identified and called 'P 2 ' by Marcos in [17].In this paper, we analyze and compare systematically the connexive variants of CSL and P 2 , obtained by adding the M3V conditional to them. Our main observations are two. First, that the inconsistency of M3V is exacerbated in the connexive variant of closed set logic, while it is attenuated in the connexive variant of the Sette-like P 2 . Second, that the M3V conditional is, unlike other conditionals, connexively stable, meaning that it remains connexive when combined with the main paraconsistent negations. * This paper was written during the COVID-19 crisis. The authors want to thank the reviewers for their precious comments, as well as the support from the PAPIIT project IG400422 and from the Notre Dame International-Mexico Faculty Grant Program project "The scope and limits of non-detachable conditionals". The first author also wants to acknowledge the support from the DGAPA-UNAM through a PASPA sabbatical grant and from the Coimbra Group and the KU Leuven through a scholarship from the Programme for Young Professors and Researchers from Latin American Universities.