Defining neurosymbolic AI

TL;DR

This paper provides a formal definition of neurosymbolic AI, unifying logical and neural representations, and clarifies the core concept of neurosymbolic inference.

Contribution

It introduces a formal, abstract definition of neurosymbolic AI and inference, clarifying the field's foundational concepts and unifying key systems under this framework.

Findings

Defines neurosymbolic inference as an integral over logical and belief functions

Abstracts key neurosymbolic AI systems within the proposed framework

Provides a formal foundation for future research in neurosymbolic AI

Abstract

Neurosymbolic AI focuses on integrating learning and reasoning, in particular, on unifying logical and neural representations. Despite the existence of an alphabet soup of neurosymbolic AI systems, the field is lacking a generally accepted formal definition of what neurosymbolic models and inference really are. We introduce a formal definition for neurosymbolic AI that makes abstraction of its key ingredients. More specifically, we define neurosymbolic inference as the computation of an integral over a product of a logical and a belief function. We show that our neurosymbolic AI definition makes abstraction of key representative neurosymbolic AI systems.