A Logic of Knowing Why
This work addresses a foundational issue in formal epistemology and AI by extending epistemic logic to include explanatory knowledge, though it is incremental as it builds on existing studies of why-questions and justification logic.
The paper tackles the problem of formalizing 'knowing why' in epistemic logic by introducing a new operator and semantics, resulting in two sound and complete axiomatizations for different introspection assumptions.
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 Ky_i operator into the language of epistemic logic to express "agent i knows why phi" and propose a Kripke-style semantics of such expressions in terms of knowing an explanation of phi. We obtain two sound and complete axiomatizations w.r.t. two different model classes depending on different assumptions about introspection.