Learning and Reasoning with Logic Tensor Networks

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 set...

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Bibliographic Details
Published inAIIA 2016 Advances in Artificial Intelligence Vol. 10037; pp. 334 - 348
Main Authors Serafini, Luciano, d’Avila Garcez, Artur S.
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2016
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Artificial intelligence
Data-driven knowledge completion
Knowledge representation
Neural-symbolic computation
Relational learning
Tensor networks
Online AccessGet full text
ISBN9783319491295
3319491296
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-49130-1_25

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Summary: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.
Bibliography:Original Abstract: 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsc {TensorFlow}^{\tiny {\text {TM}}}$$\end{document} primitives. The paper concludes with experiments on a simple but representative example of knowledge completion.
The first author acknowledges the Mobility Program of FBK, for supporting a long term visit at City University London. He also acknowledges NVIDIA Corporation for supporting this research with the donation of a GPU. We also thank Prof. Marco Gori and his group at the University of Siena for the generous and inspiring discussions on the topic of integrating logical reasoning and statistical machine learning.
ISBN:9783319491295
3319491296
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-49130-1_25