Beyond Material Implication: An Empirical Study of Residuum in Knowledge Enhanced Neural Networks

Knowledge Enchanced Neural Networks (KENN) is a neuro-symbolic architecture that exploits fuzzy logic for injecting prior knowledge, codified by propositional formulas, into a neural network. It works by adding a new layer at the end of a generic neural network that further elaborates the initial predictions accordingly to the knowledge. In the existing KENN, according to material implication rule, a conditional statement is represented as a conjunctive normal form formula. The following work extends this interpretation of the implication by using the fuzzy logic's Residuum semantic and shows how it has been integrated into the original KENN architecture, while keeping it reproducible. The Residuum integration allowed to evaluate KENN on MNIST Addition, a task that couldn't be approached by the original architecture, and the results obtained were comparable to others state of the art neuro-symbolic methods. The extended architecture has subsequently been evaluated also on visual relationships detection, showing that it could improve the performance of the original one.