News

Przemek Wałęga working with Bernardo Grau at the University of Oxford has devised a new way to prove old and new results including an open problem about graph neural networks.

Paper Title

Preservation Theorems for Unravelling-Invariant Classes: A Uniform Approach for Modal Logics and Graph Neural Networks

Abstract

We have introduced a new approach in finite model theory of modal logics for proving so-called preservation theorems. Preservation theorems form a classical research topic in model theory, which was started by famous Łoś-Tarski theorem (1954,1955). What is interesting is that we introduce a new approach that allows us, in a uniform way, to re-prove well-known results (preservation theorems by Rosen and Abramsky+Reggio), prove new results, and even solve an open problem asking about the expressive power of Monotonic Graph Neural Networks. The approach is based on a new result about well-quasi-orders on trees, which I find interesting per se.

Reference

Przemysław Andrzej Wałęga and Bernardo Cuenca Grau (2026) Preservation Theorems for Unravelling-Invariant Classes: A Uniform Approach for Modal Logics and Graph Neural Networks. arxiv.org/pdf/2602.01856