  Artificial Intelligence agents are required to learn from their surroundings
and to reason about the knowledge that has been learned in order to make
decisions. While state-of-the-art learning from data typically uses
sub-symbolic distributed representations, reasoning is normally useful at a
higher level of abstraction with the use of a first-order logic language for
knowledge representation. As a result, attempts at combining symbolic AI and
neural computation into neural-symbolic systems have been on the increase. In
this paper, we present Logic Tensor Networks (LTN), a neurosymbolic formalism
and computational model that supports learning and reasoning through the
introduction of a many-valued, end-to-end differentiable first-order logic
called Real Logic as a representation language for deep learning. We show that
LTN provides a uniform language for the specification and the computation of
several AI tasks such as data clustering, multi-label classification,
relational learning, query answering, semi-supervised learning, regression and
embedding learning. We implement and illustrate each of the above tasks with a
number of simple explanatory examples using TensorFlow 2. Keywords:
Neurosymbolic AI, Deep Learning and Reasoning, Many-valued Logic.
