 There are also versions of world-semantics for relevant logics based on Dunn’s relational semantics for FDE. Then negation is extensional. A conditional connective, now needs to be given both truth and falsity conditions. So we have: \(A \rightarrow B\) is true at \(w\) iff for all \(x, y\), such that \(Rwxy\), if \(A\) is true at \(x, B\) is true at \(y\); and \(A \rightarrow B\) is false at \(w\) iff for some \(x, y\), such that \(Rwxy\), if \(A\) is true at \(x, B\) is false at \(y\). Adding various constraints on the ternary relation provides stronger logics. However, these logics are not the standard relevant logics developed by Anderson and Belnap. To obtain the standard family of relevant logics, one needs neighbourhood frames (see Mares 2004). Further details can be found in the entry on  relevant logics.