Logic Tensor Networks

Abstract

Artificial Intelligence agents are required to learn from their surroundings and to reason about the knowledge that has been learned in order to make decisions. While state-of-the-art learning from data typically uses sub-symbolic distributed representations, reasoning is normally useful at a higher level of abstraction with the use of a first-order logic language for knowledge representation. As a result, attempts at combining symbolic AI and neural computation into neural-symbolic systems have been on the increase. In this paper, we present Logic Tensor Networks (LTN), a neurosymbolic formalism and computational model that supports learning and reasoning through the introduction of a many-valued, end-to-end differentiable first-order logic called Real Logic as a representation language for deep learning. We show that LTN provides a uniform language for the specification and the computation of several AI tasks such as data clustering, multi-label classification, relational learning, query answering, semi-supervised learning, regression and embedding learning. We implement and illustrate each of the above tasks with a number of simple explanatory examples using TensorFlow 2. Keywords: Neurosymbolic AI, Deep Learning and Reasoning, Many-valued Logic.

68 pages, 28 figures, 6 tables

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• T-Norms Driven Loss Functions for Machine Learning
• OG-SGG: Ontology-Guided Scene Graph Generation. A Case Study in Transfer Learning for Telepresence Robotics
• Analyzing Differentiable Fuzzy Logic Operators
• Reduced Implication-bias Logic Loss for Neuro-Symbolic Learning
• Representing Prior Knowledge Using Randomly, Weighted Feature Networks for Visual Relationship Detection
• Learning with Holographic Reduced Representations
• New foundations of reasoning via real-valued first-order logics