Data-driven logistics

The journey captured by this dissertation centers around knowledge compilation, model counting, and their role within state-of-the-art inference algorithms for probabilistic logic programming (PLP) languages. Model counting is the task of finding the number of solutions that satisfy a given set of constraints such as 'A or not B, and C'. Knowledge compilation techniques can reformulate these constraints such that counting becomes easier. This dissertation has four main contributions in this domain:
1) It introduces a novel improvement to model counters that enhances their performance by exploiting symmetries present within the constraints.
2) It demonstrates the general applicability of the algebraic model counting (AMC) variant, through its use within a decision making under uncertainty setting, and a synthesis of the 15-year ProbLog journey and the resulting insight that several PLP frameworks are unifiable under the same algebraic counting framework.
3) It analyzes the impact of the variable integration order on weighted model integration tasks, a counting variant that involves continuous variables, and proposes several novel ordering heuristics that significantly reduce the model integration run time.
4) It contributes to laying the foundations for knowledge compilation with respect to a background theory, which allows the use of constraints that go beyond Boolean variables, including arithmetic constraints.