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

TL;DR

This paper surveys the logical and philosophical foundations of using first-order logic in probabilistic knowledge representation, highlighting its relevance for machine learning, logical experts, and neuro-symbolic AI researchers.

Contribution

It provides a non-technical overview of the role of first-order logic in statistical relational learning and neuro-symbolic AI, clarifying concepts for diverse research communities.

Findings

Clarifies differences between finite and infinite domains.

Explains subjective probabilities versus random-world semantics.

Highlights the importance of infinite domains in probabilistic logic.

Abstract

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.