Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge
Luciano Serafini, Artur d'Avila Garcez
TL;DR
The paper tackles open-domain relational reasoning by unifying deductive logic with data-driven learning. It introduces Logic Tensor Networks (LTN) built on Real Logic, where symbols are grounded as real-valued vectors and logical constraints are enforced through neural tensor networks trained with satisfiability loss in TensorFlow. The main contributions include a principled, vector-based semantics for first-order logic, the grounded-theory formalism, and demonstrations of knowledge completion and prediction on relational data. This framework enables simultaneous reasoning and learning, offering a scalable neural-symbolic approach to knowledge completion and relational inference.
Abstract
We propose Logic Tensor Networks: a uniform framework for integrating automatic learning and reasoning. A logic formalism called Real Logic is defined on a first-order language whereby formulas have truth-value in the interval [0,1] and semantics defined concretely on the domain of real numbers. Logical constants are interpreted as feature vectors of real numbers. Real Logic promotes a well-founded integration of deductive reasoning on a knowledge-base and efficient data-driven relational machine learning. We show how Real Logic can be implemented in deep Tensor Neural Networks with the use of Google's tensorflow primitives. The paper concludes with experiments applying Logic Tensor Networks on a simple but representative example of knowledge completion.