# Coalgebra Learning via Duality

## TL;DR

This paper extends automata learning to coalgebraic structures using logical formulas and duality, providing a general algorithm with correctness and termination guarantees.

## Contribution

It introduces a coalgebraic learning framework based on duality and logic, generalizing automata learning methods to a broader class of systems.

## Key findings

- Developed an abstract coalgebra learning algorithm
- Proved the algorithm's correctness and termination
- Demonstrated learning of labelled transition systems with Hennessy-Milner logic

## Abstract

Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as tests, based on a dual adjunction between states and logical theories. This allows us to learn, e.g., labelled transition systems, using Hennessy-Milner logic. Our main contribution is an abstract learning algorithm, together with a proof of correctness and termination.