A Logic of Knowing Why

TL;DR

This paper introduces a formal logical framework for representing and reasoning about the concept of 'knowing why', extending epistemic logic with a new operator and providing sound and complete axiomatizations.

Contribution

It proposes the Ky_i operator to express 'knowing why' and develops a Kripke-style semantics with axiomatizations under different introspection assumptions.

Findings

Defined the Ky_i operator for 'knowing why'

Developed sound and complete axiomatizations

Provided semantics based on explanation models

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 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.