 One problem with the semantics without the ternary relation is that it is difficult to use it to characterize as wide a range of logical systems as can done with the ternary relation. In addition, the logics determined by this semantics are quite weak. For example, they do not have as a theorem the transitivity of implication — \(((A \rightarrow B) \amp(B \rightarrow C)) \rightarrow (A \rightarrow C)\).