Extending Logical Neural Networks using First-Order Theories
This work addresses a specific problem for researchers and practitioners in AI who use LNNs for symbolic reasoning, but it is incremental as it builds on existing LNN frameworks.
The paper tackled the limitation of Logical Neural Networks (LNNs) in handling equality and function symbols by extending them with first-order theories, resulting in the ability to reason about expressions without the unique-names assumption as demonstrated in IBM's LNN library.
Logical Neural Networks (LNNs) are a type of architecture which combine a neural network's abilities to learn and systems of formal logic's abilities to perform symbolic reasoning. LLNs provide programmers the ability to implicitly modify the underlying structure of the neural network via logical formulae. In this paper, we take advantage of this abstraction to extend LNNs to support equality and function symbols via first-order theories. This extension improves the power of LNNs by significantly increasing the types of problems they can tackle. As a proof of concept, we add support for the first-order theory of equality to IBM's LNN library and demonstrate how the introduction of this allows the LNN library to now reason about expressions without needing to make the unique-names assumption.