Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge

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 TEN- SORFLOW TM primitives. The paper concludes with experiments applying Logic Tensor Networks on a simple but representative example of knowledge completion.

Authors

• Luciano Serafini
• Artur S. d'Avila Garcez

Keywords

• Knowledge Representation
• Relational Learning
• Tensor Networks
• Neural-Symbolic Computation
• Data-driven Knowledge Completion