  Logic is the main formal language to perform automated reasoning, and it is
further a human-interpretable language, at least for small formulae. Learning
and optimising logic requirements and rules has always been an important
problem in Artificial Intelligence. State of the art Machine Learning (ML)
approaches are mostly based on gradient descent optimisation in continuous
spaces, while learning logic is framed in the discrete syntactic space of
formulae. Using continuous optimisation to learn logic properties is a
challenging problem, requiring to embed formulae in a continuous space in a
meaningful way, i.e. preserving the semantics. Current methods are able to
construct effective semantic-preserving embeddings via kernel methods (for
linear temporal logic), but the map they define is not invertible. In this work
we address this problem, learning how to invert such an embedding leveraging
deep architectures based on the Graph Variational Autoencoder framework. We
propose a novel model specifically designed for this setting, justifying our
design choices through an extensive experimental evaluation. Reported results
in the context of propositional logic are promising, and several challenges
regarding learning invertible embeddings of formulae are highlighted and
addressed.
