Insights from the Intersection of Logic and Probabilistic Reasoning

Logic and uncertainty form two of the primary pillars of modern artificial intelligence. Seeking to draw insights about what can be gained by understanding both, we explore different contexts where both are crucial. First, we use logical circuits as our underlying machinery, developing a hybrid circuit sampling technique for approximate probabilistic inference, as well as an axiomatized method for enforcing logical constraints when learning a deep neural network. We then explore modifying probabilistic databases, incorporating schema level constraints to overcome lack of data, as well as demonstrating how and why to directly incorporate them with relational machine learning techniques for free efficient inference on well tuned models