Formalize the general notion of abstraction in cognitive science and artificial intelligence

Develop a principled formalization of the general notion of abstraction across cognitive science and artificial intelligence, providing a precise, rigorous framework that captures how hierarchical structures in systems correspond to hierarchical belief states and enables tractable inference in partially observable settings.

Background

The paper introduces symmetry-induced abstract beliefs that can be updated autonomously at different levels of resolution, mirroring objective hierarchies in dynamical systems. This contributes toward formalizing abstraction by linking system symmetries to coarse-grained inference.

Despite these advances, the authors explicitly acknowledge that a comprehensive, principled formalization of abstraction is a fundamental open problem spanning cognitive science and artificial intelligence.