Logical Neural Networks

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.

10 pages (incl. references), 38 pages supplementary, 7 figures, 9 tables, 6 algorithms. In submission to NeurIPS 2020

References in corpus (2)

• Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge
• TensorLog: A Differentiable Deductive Database

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• Towards Safe Autonomous Driving Policies using a Neuro-Symbolic Deep Reinforcement Learning Approach
• Differentiable Inductive Logic Programming for Structured Examples
• Non-Parametric Neuro-Adaptive Control Subject to Task Specifications
• Automated and Explainable Ontology Extension Based on Deep Learning: A Case Study in the Chemical Domain
• Logical Credal Networks
• Combining Rules and Embeddings via Neuro-Symbolic AI for Knowledge Base Completion
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• Deep Algorithmic Question Answering: Towards a Compositionally Hybrid AI for Algorithmic Reasoning
• Understanding in Artificial Intelligence
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