Samy Badreddine

The field of neuro-symbolic artificial intelligence (NeSy), which combines learning and reasoning, has recently experienced significant growth. There now are a wide variety of NeSy frameworks , each with its own specific language for expressing background knowledge and how to relate it to neural networks. This heterogeneity hinders accessibility for newcomers and makes comparing different NeSy frameworks challenging. We propose a unified language for NeSy, which we call ULLER, a Unified Language for LEarning and Reasoning. ULLER encompasses a wide variety of settings, while ensuring that knowledge described in it can be used in existing NeSy systems. ULLER has a neuro-symbolic first-order syntax for which we provide example semantics including classical, fuzzy, and probabilistic logics. We believe ULLER is a first step towards making NeSy research more accessible and comparable, paving the way for libraries that streamline training and evaluation across a multitude of semantics, knowledge bases, and NeSy systems.

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.