 An approach to relevance that does not require the ternary relation is due to Routley and Loparic (1978) and Priest (1992) and (2008). This semantics uses a set of worlds and a binary relation, \(S\). Worlds are divided into two categories: normal worlds and non-normmal worlds. An implication \(A \rightarrow B\) is true at a normal world \(a\) if and only if for all worlds \(b\), if \(A\) is true at \(b\) then \(B\) is also true true at \(b\). At non-normal worlds, the truth values for implications are random. Some may be true and others false. A formula is valid if and only if it is true on every such model in its normal worlds. This division of worlds into normal and non-normal and the use of random truth values for implications at non-normal worlds enables us to find countermodels for formulas such as \(p \rightarrow  (q \rightarrow q)\).