  The large and still increasing popularity of deep learning clashes with a
major limit of neural network architectures, that consists in their lack of
capability in providing human-understandable motivations of their decisions. In
situations in which the machine is expected to support the decision of human
experts, providing a comprehensible explanation is a feature of crucial
importance. The language used to communicate the explanations must be formal
enough to be implementable in a machine and friendly enough to be
understandable by a wide audience. In this paper, we propose a general approach
to Explainable Artificial Intelligence in the case of neural architectures,
showing how a mindful design of the networks leads to a family of interpretable
deep learning models called Logic Explained Networks (LENs). LENs only require
their inputs to be human-understandable predicates, and they provide
explanations in terms of simple First-Order Logic (FOL) formulas involving such
predicates. LENs are general enough to cover a large number of scenarios.
Amongst them, we consider the case in which LENs are directly used as special
classifiers with the capability of being explainable, or when they act as
additional networks with the role of creating the conditions for making a
black-box classifier explainable by FOL formulas. Despite supervised learning
problems are mostly emphasized, we also show that LENs can learn and provide
explanations in unsupervised learning settings. Experimental results on several
datasets and tasks show that LENs may yield better classifications than
established white-box models, such as decision trees and Bayesian rule lists,
while providing more compact and meaningful explanations.
