Grounding rules for (relevant) implication

Abstract

In Poggiolesi [(2020a). Grounding principles for (relevant) implication. Synthese, 1–28], a definition of the notion of grounding in the background of a relevant framework has been introduced; this definition generates some intuitively acceptable grounding principles for relevant implication. In the present paper, our aim is to construct a logic based on that definition. Our logic will be a calculus of natural deduction and will formalise the relation of grounding both as a meta-linguistic relation and as a connective. The calculus will contain grounding rules for relevant implication and will be proved to be sound and complete with respect to the original definition. Finally we will prove the deduction theorem at the grounding level.