Graph Neural Networks as the Copula Mundi between Logic and Machine Learning: A Roadmap

Combining machine learning (ML) and computational logic (CL) is hard, mostly because of the inherently-different ways they use to represent knowledge. In fact, while ML relies on fixed-size numeric representations leveraging on vectors, matrices, or tensors of real numbers, CL relies on logic terms and clauses—which are unlimited in size and structure.
Graph neural networks (GNN) are a novelty in the ML world introduced for dealing with graph-structured data in a sub-symbolic way. In other words, GNN pave the way towards the application of ML to logic clauses and knowledge bases. However, there are several ways to encode logic knowledge into graphs: which is the best one heavily depends on the specific task at hand.
Accordingly, in this paper, we (i) elicit a number of problems from the field of CL that may benefit from many graph-related problems where GNN has been proved effective; (ii) exemplify the application of GNN to logic theories via an end-to-end toy example, to demonstrate the many intricacies hidden behind the technique; (iii) discuss the possible future directions of the application of GNN to CL in general, pointing out opportunities and open issues.

keywords   Graph Neural Networks, Machine Learning, Embedding, Computational Logic

reference talk

 Graph Neural Networks as the Copula Mundi between Logic and Machine Learning: a Roadmap (WOA 2021, 02/09/2021) — Andrea Agiollo (Andrea Agiollo, Giovanni Ciatto, Andrea Omicini)

origin event

 WOA 2021

container publication

 WOA 2021 – 22nd Workshop “From Objects to Agents” (edited volume, 2021) — Roberta Calegari, Giovanni Ciatto, Enrico Denti, Andrea Omicini, Giovanni Sartor

funding project

 EXPECTATION — Personalized Explainable Artificial Intelligence for decentralized agents with heterogeneous knowledge (01/04/2021–31/03/2024)

 StairwAI — Stairway to AI: Ease the Engagement of Low-Tech users to the AI-on-Demand platform through AI (01/01/2021–31/12/2023)

reference publication for talk

 Graph Neural Networks as the Copula Mundi between Logic and Machine Learning: a Roadmap (WOA 2021, 02/09/2021) — Andrea Agiollo (Andrea Agiollo, Giovanni Ciatto, Andrea Omicini)