This tutorial will provide a gentle introduction into the foundations of statistical relational artificial intelligence, and will realize this by introducing the foundations of logic, of probability, of learning, and their respective combinations. Both predicate logic and probability theory extend propositional logic, one by adding relations, individuals and quantified variables, the other by allowing for measures over possible worlds and conditional queries. While logical and probabilistic approaches have often been studied and used independently within artificial intelligence, they are not in conflict with each other but they are synergistic. This explains why there has been a considerable body of research in combining first-order logic and probability over the last 25 years, evolving into what has come to be called Statistical Relational Artificial Intelligence (StarAI).
Relational probabilistic models — we use this term in the broad sense, meaning any models that combine relations and probabilities — form the basis of StarAI, and can be seen as combinations of probability and predicate calculus that allow for individuals and relations as well as probabilities. In building on top of relational models, StarAI goes far beyond reasoning, optimization, learning and acting optimally in terms of a fixed number of features or variables, as it is typically studied in machine learning, constraint satisfaction, probabilistic reasoning, and other areas of AI. Since StarAI draws upon ideas developed within many different fields, however, it can also be quite challenging for newcomers to get started and our tutorial precisely aims to provide this background.