---
title: "Grounding Methods for Neural-Symbolic AI"
authors:
  - "Rodrigo Castellano Ontiveros"
  - "Francesco Giannini"
  - "Marco Gori"
  - "Giuseppe Marra"
  - "Michelangelo Diligenti"
doi: "10.24963/ijcai.2025/535"
url: "https://ijcai.org/proceedings/2025/535"
pdf: "https://ijcai.org/proceedings/2025/0535.pdf"
venue: "Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"
year: 2025
pages: "4806-4814"
track: "Main Track"
keywords:
  - "Machine Learning: ML: Neuro-symbolic methods/Abductive Learning"
  - "Knowledge Representation and Reasoning: KRR: Learning and reasoning"
---

# Grounding Methods for Neural-Symbolic AI

Rodrigo Castellano Ontiveros, Francesco Giannini, Marco Gori, Giuseppe Marra, Michelangelo Diligenti

*Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence*, pages 4806-4814. DOI: [10.24963/ijcai.2025/535](https://doi.org/10.24963/ijcai.2025/535)

## Abstract

A large class of Neural-Symbolic (NeSy) methods employs a machine learner to process the input entities, while relying on a reasoner based on First-Order Logic to represent and process more complex relationships among the entities. A fundamental role for these methods is played by the process of logic grounding, which determines the relevant substitutions for the logic rules using a (sub)set of entities.
Some NeSy methods use an exhaustive derivation of all possible substitutions, preserving the full expressive power of the logic knowledge, but leading to a combinatorial explosion of the number of ground formulas to consider and, therefore, strongly limiting their scalability. Other methods rely on heuristic-based selective derivations, which are generally more computationally efficient, but lack a justification and provide no guarantees of preserving the information provided to and returned by the reasoner. 
Taking inspiration from multi-hop symbolic reasoning, this paper proposes a parametrized family of grounding methods generalizing classic Backward Chaining. Different selections within this family allow to obtain commonly employed grounding methods as special cases, and to control the trade-off between expressiveness and scalability of the reasoner.
The experimental results show that the selection of the grounding criterion is often as important as the NeSy method itself.