# Learning Syllogism with Euler Neural-Networks

arXiv: https://arxiv.org/abs/2007.07320 · HTML: https://mlsanity.com/paper/2007.07320/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Exploring Reasoning Biases in Large Language Models Through Syllogism: Insights from the NeuBAROCO Dataset](https://mlsanity.com/paper/2408.04403/) (2024)
- [Categorical Syllogisms Revisited: A Review of the Logical Reasoning Abilities of LLMs for Analyzing Categorical Syllogism](https://mlsanity.com/paper/2406.18762/) (2024)
- [Abductive Reasoning with Syllogistic Forms in Large Language Models](https://mlsanity.com/paper/2603.06428/) (2026)
- [A Syllogistic Probe: Tracing the Evolution of Logic Reasoning in Large Language Models](https://mlsanity.com/paper/2601.17426/) (2026)

## Abstract (arXiv)

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.