An Algebraic Approach to Weighted Answer-set Programming

Logic programs, more specifically, Answer-set programs, can be annotated with probabilities on facts to express uncertainty. We address the problem of propagating weight annotations on facts (eg probabilities) of an ASP to its standard models, and from there to events (defined as sets of atoms) in a dataset over the program's domain. We propose a novel approach which is algebraic in the sense that it relies on an equivalence relation over the set of events. Uncertainty is then described as polynomial expressions over variables. We propagate the weight function in the space of models and events, rather than doing so within the syntax of the program. As evidence that our approach is sound, we show that certain facts behave as expected. Our approach allows us to investigate weight annotated programs and to determine how suitable a given one is for modeling a given dataset containing events.