# A Logic of Knowing Why

arXiv: https://arxiv.org/abs/1609.06405 · HTML: https://mlsanity.com/paper/1609.06405/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2016.

## Built on by (most cited first, 3 of 3)

- [Providing personalized Explanations: a Conversational Approach](https://mlsanity.com/paper/2307.11452/) (2023)
- [Tableaux for the Logic of Strategically Knowing How](https://mlsanity.com/paper/2307.05066/) (2023)
- [Better Understanding, Understanding Better](https://mlsanity.com/paper/2606.31892/) (2026)

## Abstract (arXiv)

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.