 Albeit according to Routley (1978), Routley et al. (1982) and Routley and Routley (1985) there is a close relation between connexive logic and the idea of negation as cancellation, Routley suggested a semantics using a generation relation and the star negation in ternary frames for relevance logics, whereas connexive logics based in a straightforward way on the cancellation view of negation have been worked out by Priest (1999). Priest (1999) directly translates a definition of entailment that enforces the null-content account of contradictions into evaluation clauses. A model is a structure M = &lt;W, g, v&gt;, where W is a non-empty set of possible worlds, g is a distinguished element from W, and v is a valuation function from the set of propositional variables into the set of classical truth values {1, 0}. Two clauses for evaluating implications at possible worlds are considered (notation adjusted):