Logical Neural Networks

2020/06/23 by Ryan Riegel, Riegel, Ryan, Alexander Gray +28 · 1 voice · 84 citations
Computer Science · Mathematics · #Artificial Intelligence (cs.AI) #Artificial intelligence #Artificial neural network #Bayesian Modeling and Causal Inference #Computer science #Contradiction #Differentiable function #Discrete mathematics #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Function (biology) #Inference #Knowledge representation and reasoning #Logic in Computer Science (cs.LO) #Machine Learning (cs.LG) #Mathematics #Neural Networks and Applications #Principle of compositionality #Probabilistic logic #Programming language #Pure mathematics #Representation (politics) #Representation theorem #Semantics (computer science) #Theoretical computer science #cs.AI #cs.LG #cs.LO

paper · pdf · doi:10.48550/arxiv.2006.13155

published in arXiv (Cornell University) (Cornell University) · 10 pages (incl. references), 38 pages supplementary, 7 figures, 9 tables, 6 algorithms. In submission to NeurIPS 2020

arxiv created 2020/06/23 · openalex publication_date 2020/06/23 · arxiv published 2020/06/23 · arxiv updated 2020/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.

Citations

• Artificial intelligence: a modern approach
• TensorLog: A Differentiable Deductive Database

Cited by

• Modal Logical Neural Networks
• Concept-RuleNet: Grounded Multi-Agent Neurosymbolic Reasoning in Vision Language Models
• COCO-Tree: Compositional Hierarchical Concept Trees for Enhanced Reasoning in Vision Language Models
• Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration
• Rethinking Explainable Disease Prediction: Synergizing Accuracy and Reliability via Reflective Cognitive Architecture
• Łukasiewicz Logic with Actions for Neural Networks training
• Lattice Annotated Temporal (LAT) Logic for Non-Markovian Reasoning
• Understanding in Artificial Intelligence
• Reasoning in Computer Vision: Taxonomy, Models, Tasks, and Methodologies
• Neural Logic Networks for Interpretable Classification
• A Comparative Study of Neurosymbolic AI Approaches to Interpretable Logical Reasoning
• pix2rule: End-to-end Neuro-symbolic Rule Learning
• Logic Embeddings for Complex Query Answering
• Learning Interpretable Differentiable Logic Networks for Tabular Regression
• Reliable Natural Language Understanding with Large Language Models and Answer Set Programming
• Combining Rules and Embeddings via Neuro-Symbolic AI for Knowledge Base Completion
• Modular Machine Learning: An Indispensable Path towards New-Generation Large Language Models

Discussions

• I think these two recent papers of his are somewhat representative of the intended direction: Logical neural networks arxiv.org/abs/2006.13155 What makes models compositional? arxiv.org/abs/2405.02 [bsky, 0 points, 0 comments]

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• DeepLogic: Towards End-to-End Differentiable Logical Reasoning
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