What is Relevant Implication?

Abstract

In the work of Anderson and Belnap on entailment logics relevance rather than modality emerged as the central concept (though modality is emphasized in one of Ackermann’s early papers). In the present paper I propose to investigate this concept through three closely connected analyses, one proof-theoretical, the other two semantical. On the strength of these analyses I defend a concept of relevant implication which is intuitionistic rather than classical (as in the work of Anderson, Belnap, Meyer, Dunn and others).