A Logical Framework for Understanding Why

Epistemic logic pays barely any attention to the notion of understanding, which stands in total contrast to the current situation in epistemology and in philosophy of science. This paper studies understanding why in an epistemic-logic-style. It is generally acknowledged that understanding why moves beyond knowing why. Inspired by philosophical ideas, we consider whereas knowing why requires knowing horizontal explanations, understanding why additionally requires vertical explanations. Based on justification logic and existing logical work for knowing why, we build up a framework by introducing vertical explanations, and show it could accommodate different philosophical viewpoints via adding conditions to the models. A sound and complete axiomatization for the most general case is given.