Logical Neural Networks

2020/06/23 by Ryan Riegel, Riegel, Ryan, Alexander Gray +27 · 13 citations
Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Machine Learning (cs.LG) #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2006.13155

openalex publication_date 2020/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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
• Grounding AI Explanations in Experience: A Reflective Cognitive Architecture for Clinical Decision Support
• 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

Related

• Neural Logic Machines
• DeepLogic: Towards End-to-End Differentiable Logical Reasoning
• Neuro-symbolic Learning Yielding Logical Constraints
• Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks
• Logical Boltzmann Machines