  We present VAEL, a neuro-symbolic generative model integrating variational
autoencoders (VAE) with the reasoning capabilities of probabilistic logic (L)
programming. Besides standard latent subsymbolic variables, our model exploits
a probabilistic logic program to define a further structured representation,
which is used for logical reasoning. The entire process is end-to-end
differentiable. Once trained, VAEL can solve new unseen generation tasks by (i)
leveraging the previously acquired knowledge encoded in the neural component
and (ii) exploiting new logical programs on the structured latent space. Our
experiments provide support on the benefits of this neuro-symbolic integration
both in terms of task generalization and data efficiency. To the best of our
knowledge, this work is the first to propose a general-purpose end-to-end
framework integrating probabilistic logic programming into a deep generative
model.
