 One useful addition to the relevant theory of quantification is a conditional that is used to represent restricted quantification. This is developed by Jc Beall, et al. (2006). Consider the categorial scheme, “All \(A\)s are \(B\)s”. This scheme is translated into the language of classical logic as \(\forall x(A(x)\supset B(x))\). The material conditional, \(\supset\), is too weak to do this job in relevant logic (where \(A\supset B\) is understood as \(\neg A\vee B)\). If we were to use material implication is this manner, in a model for relevant logic, we could have a world in which all \(A\)s are \(B\)s, and some \(i\) is \(A\), but where \(i\) is not \(B\). The material conditional is too weak, but relevant implication is too strong. When one says, for example, “Everyone in this room owns a dog”, she does not mean that it follows from being in this room that people own a dog. Rather, it just happens that every person in this room owns a dog. It is this connection, that lies somewhere between material and relevant implication that the restricted quantificational conditional is supposed to capture. 