Over the last years, there has been increasing research on the scaling behaviour of statistical relational representations with the size of the domain, and on the connections between domain size dependence and lifted inference. In particular, the asymptotic behaviour of statistical relational representations has come under scrutiny, and projectivity was isolated as the strongest form of domain size independence. In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to a probabilistic logic program consisting only of range-restricted clauses over probabilistic facts. To facilitate the application of classical results from finite model theory, we introduce the abstract distribution semantics, defined as an arbitrary logical theory over probabilistic facts to bridge the gap to the distribution semantics underlying probabilistic logic programming. In this representation, range-restricted logic programs correspond to quantifier-free theories, making asymptotic quantifier results avilable for use. We can conclude that every probabilistic logic program inducing a projective family of distributions is in fact captured by this class, and we can infer interesting consequences for the expressivity of probabilistic logic programs as well as for the asymptotic behaviour of probabilistic rules.

中文翻译：

---

概率逻辑编程的渐近分析，对表示投影分布族有影响

在过去的几年中，关于统计关系表示随域大小的缩放行为以及域大小依赖性和提升的推理之间的联系的研究越来越多。特别是，统计关系表示的渐近行为已受到严格审查，而射影性则被认为是域大小独立性的最强形式。在此贡献中，我们显示了分布语义下的每个概率逻辑程序在渐近性上都等同于仅由概率事实范围限制子句组成的概率逻辑程序。为了促进有限模型理论对经典结果的应用，我们引入了抽象分布语义，定义为关于概率事实的任意逻辑理论，以弥合与概率逻辑编程基础的分布语义之间的差距。在这种表示形式中，范围受限的逻辑程序对应于无量词的理论，使得渐近量词的结果可供使用。我们可以得出结论，该类实际上捕获了每个引起投影分布族的概率逻辑程序，并且我们可以推断出概率逻辑程序的表达性以及概率规则的渐近行为的有趣结果。