In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for machine learning researchers unaware of why the research community cares about relational representations, this article can serve as a gentle introduction. Second, for logical experts who are newcomers to the learning area, such an article can help in navigating the differences between finite vs infinite, and subjective probabilities vs random-world semantics. Finally, for researchers from statistical relational learning and neuro-symbolic AI, who are usually embedded in finite worlds with subjective probabilities, appreciating what infinite domains and random-world semantics brings to the table is of utmost theoretical import.

翻译：本文旨在以非技术性的方式简要阐述并梳理使用（一阶）逻辑表示（概率）知识的逻辑与哲学基础。我们的动机有三：首先，对于不了解研究界为何关注关系表示法的机器学习研究者，本文可作为温和的入门指南；其次，对于初涉学习领域的逻辑学专家，本文有助于理解有限与无限、主观概率与随机世界语义之间的差异；最后，对于通常深耕于有限世界和主观概率假设的统计关系学习与神经符号AI研究者，理解无限域和随机世界语义带来的理论价值具有极其重要的学术意义。