 The starting point for Hitoshi Omori’s (2016a) definition of a connexive extension of the basic relevance logic BD (see the entry  logic: relevance)  is to find a proof theory for extensions of BD with negation treated according to the American Plan. Priest and Sylvan (1992) posed this as an open problem, and Omori gives a partial solution by defining a connexive variant BDW of BD. The semantics uses models based on ternary frames. There is a base state g, the four truth values are represented as subsets of the set of classical truth values {0,1}, and interpretations are defined in the style of Dunn (cf. Omori and Wansing 2017). A model is quadruple &lt;g, W, R, I&gt;, where W is a non-empty set (of states), g∈W, R is a three-place relation on W with Rgxy iff x = y, and I is a function that maps pairs consisting of a state and a propositional variable to subsets of {0,1}. The interpretation function I is then extended to an assignment of truth values at states for all formulas as follows: