IID Relaxation by Logical Expressivity: A Research Agenda for Fitting Logics to Neurosymbolic Requirements

TL;DR

This paper proposes a research agenda to analyze how relaxing the IID assumption using logical expressivity can benefit Neurosymbolic AI by leveraging data dependencies and distribution constraints.

Contribution

It introduces a hierarchy of logics tailored to different Neurosymbolic use cases, emphasizing the importance of logical expressivity in modeling data dependencies.

Findings

Exploiting data dependencies improves Neurosymbolic reasoning.

Logical expressivity influences ML routine design.

A new research agenda for relaxing IID assumptions in logic-based AI.

Abstract

Neurosymbolic background knowledge and the expressivity required of its logic can break Machine Learning assumptions about data Independence and Identical Distribution. In this position paper we propose to analyze IID relaxation in a hierarchy of logics that fit different use case requirements. We discuss the benefits of exploiting known data dependencies and distribution constraints for Neurosymbolic use cases and argue that the expressivity required for this knowledge has implications for the design of underlying ML routines. This opens a new research agenda with general questions about Neurosymbolic background knowledge and the expressivity required of its logic.