New Relevant Logic ER

Relevant logic has been researched for removal of the fallacies of implication from classical logic. Many kinds of relevant logics have been proposed, but these logics are weaker than necessary and un-suitable for the formalization of knowledge reasoning. This paper presents a new relevant logic ER. We give two characteristics of ER; the first is that variable-sharing, which is a necessary condition for relevant logics, holds in ER, and the second is that ER excludes fallacies of relation and validity, which are considered to be strong fallacies and removed from most relevant logics. Further, we show that ER is a stronger logic than the typical relevant logic R, espe-cially, some classical logic theorems that can not be inferred in R and do not include fallacies can be inferred in ER. It follows that ER is more suitable for formalization of knowledge reasoning.