A logic of knowing why

Abstract

When we say “I know why he was late”, we know not only the fact that he was late, but also an explanation of this fact. We propose a logical framework of “knowing why” inspired by the existing formal studies on why-questions, scientific explanation, and justification logic. We introduce the $${{\mathcal {K}}{}\textit{y}}_i$$ operator into the language of epistemic logic to express “agent i knows why $$\varphi $$ ” and propose a Kripke-style semantics of such expressions in terms of knowing an explanation of $$\varphi $$ . We obtain two sound and complete axiomatizations w.r.t. two different model classes depending on different assumptions about introspection. Finally we connect our logic with justification logic technically by providing an alternative semantics and an in-depth comparison on various design choices.