Logic Tensor Networks

Attempts at combining logic and neural networks into neurosymbolic approaches have been on the increase in recent years. In a neurosymbolic system, symbolic knowledge assists deep learning, which typically uses a sub-symbolic distributed representation, to learn and reason at a higher level of abstraction. We present Logic Tensor Networks (LTN), a neurosymbolic framework that supports querying, learning and reasoning with both rich data and abstract knowledge about the world. LTN introduces a fully differentiable logical language, called Real Logic, whereby the elements of a first-order logic signature are grounded onto data using neural computational graphs and first-order fuzzy logic semantics. We show that LTN provides a uniform language to represent and compute efficiently many of the most important AI tasks such as multi-label classification, relational learning, data clustering, semi-supervised learning, regression, embedding learning and query answering. We implement and illustrate each of the above tasks with several simple explanatory examples using TensorFlow 2. The results indicate that LTN can be a general and powerful framework for neurosymbolic AI. (c) 2021 Elsevier B.V. All rights reserved. (C) 2021 Elsevier B.V. All rights reserved.