Grounding Methods for Neural-Symbolic AI

TL;DR

This paper introduces a flexible family of grounding methods for Neural-Symbolic AI that balances expressiveness and scalability, inspired by multi-hop reasoning and generalizing classic Backward Chaining.

Contribution

It proposes a parametrized framework for logic grounding in NeSy systems, unifying existing methods and enabling controlled trade-offs between efficiency and expressiveness.

Findings

Grounding method choice significantly impacts NeSy performance.

The proposed family includes common grounding approaches as special cases.

Experimental results demonstrate the importance of grounding criteria selection.

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. This leads to a combinatorial explosion in the number of ground formulas to consider and, therefore, strongly limits 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 us 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.