Defining Formal Explanation in Classical Logic by Substructural Derivability

Precisely framing a formal notion of explanation is a hard problem of great relevance for several areas of scientific investigation such as computer science, philosophy and mathematics. We study a notion of formal explanation according to which an explanation of a formula F must contain all and only the true formulae that concur in determining the truth of F. Even though this notion of formal explanation is defined by reference to derivability in classical logic, the relation that holds between the explained formula and the formulae explaining it has a distinct substructural flavour, due to the fact that no redundancy is admitted among the explaining formulae. We formalise this intuition and prove that this notion of formal explanation is essentially connected, in a very specific sense, to derivability in a substructural calculus.