Learning and Reasoning with Logic Tensor Networks

• Published in: AIIA 2016 Advances in Artificial Intelligence Vol. 10037; pp. 334 - 348
• Main Authors: Serafini, Luciano, d’Avila Garcez, Artur S.
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2016; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Artificial intelligence; Data-driven knowledge completion; Knowledge representation; Neural-symbolic computation; Relational learning; Tensor networks
• ISBN: 9783319491295; 3319491296
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-49130-1_25

The paper introduces real logic: a framework that seamlessly integrates logical deductive reasoning with efficient, data-driven relational learning. Real logic is based on full first order language. Terms are interpreted in n-dimensional feature vectors, while predicates are interpreted in fuzzy sets. In real logic it is possible to formally define the following two tasks: (i) learning from data in presence of logical constraints, and (ii) reasoning on formulas exploiting concrete data. We implement real logic in an deep learning architecture, called logic tensor networks, based on Google’s $$\textsc {TensorFlow}^{\tiny {\text {TM}}}$$ primitives. The paper concludes with experiments on a simple but representative example of knowledge completion.