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.

翻译：逻辑程序，更具体而言，答案集程序，可以通过在事实上标注概率来表达不确定性。我们研究了将ASP事实上的权重标注（例如概率）传播至其标准模型，并进一步传播至定义在程序域上数据集中的事件（定义为原子集合）的问题。我们提出了一种新颖的代数方法，其核心在于建立事件集合上的等价关系。不确定性被描述为基于变量的多项式表达式。我们通过在模型和事件空间中传播权重函数，而非在程序语法内部进行操作。作为方法可靠性的证据，我们证明了特定事实的行为符合预期。该方法使我们能够研究带权重标注的程序，并评估特定程序对包含事件的数据集进行建模的适用性。