 By itself, the use of the ternary relation is not sufficient to avoid all the paradoxes of implication. Given what we have said so far, it is not clear how the semantics can avoid paradoxes such as \((p \amp \neg p) \rightarrow q\) and \(p \rightarrow  (q \vee \neg q)\). These paradoxes are avoided by the inclusion of inconsistent and non-bivalent worlds in the semantics. For, if there were no worlds at which \(p \amp \neg p\) holds, then, according to our truth condition for the arrow, \((p \amp \neg p) \rightarrow q\) would also hold everywhere. Likewise, if \(q \vee \neg q\) held at every world, then \(p \rightarrow(q \vee \neg q)\) would be universally true.