We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as resolving inconsistencies in answer set programs, ranking stable models, associating probability to stable models, and applying statistical inference to computing weighted stable models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.

翻译：本文遵循马尔可夫逻辑的对数线性模型，在稳定模型语义下引入加权规则的概念。这为克服稳定模型语义的确定性本质提供了多种方法，例如消除回答集程序中的不一致性、对稳定模型进行排序、为稳定模型赋予概率，以及将统计推断应用于加权稳定模型的计算。我们还与相关形式体系（如回答集程序、马尔可夫逻辑、ProbLog和P-log）进行了形式化比较。