ABSTRACT
Let us start with relevance. The thought that there must be some connection between the antecedent and consequent of a true conditional is an ancient and very natural one. A (prepositional) relevant logic is one which respects this intuition in the following form: whenever A -> B is a logical truth, A and B share a prepositional parameter. In particular, then, ¥ (p A -<p) -¥ q. Strictly speaking, relevant logics need not be paraconsistent. For example, Ackermann's system II' was relevant. However, one of its primitive rules was the disjunctive syllogism, and (interpreting this as a rule of derivability) it quickly gives p, ->p t= q. Still, the same kind of intuition that rebels against the logical truth of conditionals of the form (p A -ip) —> q rebels against the validity of inferences of the form p, -\p h q. It is not, therefore, surprising that most relevant logics are paraconsistent as well. Indeed, Ackermann's II' was reworked by Anderson and Belnap into their favourite relevant logic, E, which is paraconsistent.
