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Understanding Characteristics of Evolved Instances for State-of-the-Art Inexact TSP Solvers with Maximum Performance Difference Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Learning and Reasoning with Logic Tensor Networks

Authors : Luciano Serafini, Artur S. d’Avila Garcez

Published in: AI*IA 2016 Advances in Artificial Intelligence

Publisher: Springer International Publishing

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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 \(\textsc {TensorFlow}^{\tiny {\text {TM}}}\) primitives. The paper concludes with experiments on a simple but representative example of knowledge completion.

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Footnotes
1
In logic, the term “grounding” indicates the operation of replacing the variables of a term/formula with constants, or terms that do not contains other variables. To avoid confusion, we use the synonym “instantiation” for this sense.
 
3
Normally, a probabilistic approach is taken to solve this problem, and one that requires instantiating all clauses to remove variables, essentially turning the problem into a propositional one; ltn takes a different approach.
 
4
Notice how no grounding is provided about the signature of the knowledge-base.
 
5
A smoth factor \(\lambda ||\mathbf {\Omega }||^2_2\) is added to the loss to limit the size of parameters.
 
6
\(\mu (a,b) = \min (1,a+b)\).
 
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Metadata
Title
Learning and Reasoning with Logic Tensor Networks
Authors
Luciano Serafini
Artur S. d’Avila Garcez
Copyright Year
2016
Book
AI*IA 2016 Advances in Artificial Intelligence

Print ISBN: 978-3-319-49129-5

Electronic ISBN: 978-3-319-49130-1

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-49130-1_25

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