Categorical Propositions In Relevance Logic

Abstract

While 'Men are a subset of mortals' goes over into classical formal implication in relevance logic, 'All men are mortal' poses a problem. It is neither a generalized relevant conditional nor a generalized intuitionistic conditional. Restricted quantification doesn't really help either. Categoricals must rather be construed as generalized conditional assertions in the sense of Nuel D Belnap Jr. and Ruth Manor. The task indicated is thus to extend relevance logic to include conditional assertion.