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

Statistical relational learning and neuro-symbolic AI: what does first-order logic offer?