# Better Understanding, Understanding Better

arXiv: https://arxiv.org/abs/2606.31892 · HTML: https://mlsanity.com/paper/2606.31892/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 36 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [The Debate Over Understanding in AI's Large Language Models](https://mlsanity.com/paper/2210.13966/) (2022)
- [Mechanistic Indicators of Understanding in Large Language Models](https://mlsanity.com/paper/2507.08017/) (2025)
- [Beyond knowing that: a new generation of epistemic logics](https://mlsanity.com/paper/1605.01995/) (2016)
- [A Logic of Knowing Why](https://mlsanity.com/paper/1609.06405/) (2016)

## Abstract (arXiv)

"Any fool can know; the point is to understand." A well-known remark often attributed to Einstein captures a widely shared intuition: understanding is more than merely knowing. Yet epistemic logic has paid relatively little attention to understanding, despite its central role in contemporary epistemology, philosophy of science, and recent debates about AI. A recurring theme in the philosophical literature is that, unlike knowledge, understanding comes in degrees: one may understand something more or less well, and one's understanding may be better than another's. We introduce a comparative epistemic logic of understanding with level-indexed understanding modalities and a comparative connective for saying that one agent understands why a proposition better than another agent does. Semantically, we enrich multi-agent epistemic models with agent-indexed graded explanation structures and a justification-style term algebra. This yields a unified framework for representing minimal, ordinary, more demanding, and ideal understanding, together with comparisons between agents with respect to the same formula at issue. We distinguish a finitary bounded-level calculus from an infinitary full-language companion system. We establish soundness and strong completeness, and show that each fixed finite-level fragment is decidable.