Logic meets Probability: Towards Explainable AI Systems for Uncertain Worlds

Logical AI is concerned with formal languages to represent and reason with qualitative specifications; statistical AI is concerned with learning quantitative specifications from data. To combine the strengths of these two camps, there has been exciting recent progress on unifying logic and probability. We review the many guises for this union, while emphasizing the need for a formal language to represent a system's knowledge. Formal languages allow their internal properties to be robustly scrutinized, can be augmented by adding new knowledge, and are amenable to abstractions, all of which are vital to the design of intelligent systems that are explainable and interpretable.