Learning Syllogism with Euler Neural-Networks
This addresses the limitation of traditional neural networks in logical reasoning for AI systems, though it is incremental as it builds on existing neural network concepts with a novel topological approach.
The paper tackles the problem of logical reasoning in neural networks by proposing Euler Neural-Networks (ENN), which represent concepts as balls to learn topological configurations as Euler diagrams, enabling precise representation of all 24 syllogism structures and showing superior performance on datasets from WordNet-3.0 and DBpedia.
Traditional neural networks represent everything as a vector, and are able to approximate a subset of logical reasoning to a certain degree. As basic logic relations are better represented by topological relations between regions, we propose a novel neural network that represents everything as a ball and is able to learn topological configuration as an Euler diagram. So comes the name Euler Neural-Network (ENN). The central vector of a ball is a vector that can inherit representation power of traditional neural network. ENN distinguishes four spatial statuses between balls, namely, being disconnected, being partially overlapped, being part of, being inverse part of. Within each status, ideal values are defined for efficient reasoning. A novel back-propagation algorithm with six Rectified Spatial Units (ReSU) can optimize an Euler diagram representing logical premises, from which logical conclusion can be deduced. In contrast to traditional neural network, ENN can precisely represent all 24 different structures of Syllogism. Two large datasets are created: one extracted from WordNet-3.0 covers all types of Syllogism reasoning, the other extracted all family relations from DBpedia. Experiment results approve the superior power of ENN in logical representation and reasoning. Datasets and source code are available upon request.