  We propose Logic Tensor Networks: a uniform framework for integrating
automatic learning and reasoning. A logic formalism called Real Logic is
defined on a first-order language whereby formulas have truth-value in the
interval [0,1] and semantics defined concretely on the domain of real numbers.
Logical constants are interpreted as feature vectors of real numbers. Real
Logic promotes a well-founded integration of deductive reasoning on a
knowledge-base and efficient data-driven relational machine learning. We show
how Real Logic can be implemented in deep Tensor Neural Networks with the use
of Google's tensorflow primitives. The paper concludes with experiments
applying Logic Tensor Networks on a simple but representative example of
knowledge completion.
