Types of Relations: Defining Analogies with Category Theory

TL;DR

This paper introduces a formal framework using category theory to represent knowledge domains and construct analogies, enabling better understanding and transfer of knowledge in AI and human cognition.

Contribution

It formalizes knowledge domains as categories and employs categorical constructs like functors, pullbacks, and pushouts to define and analyze analogies.

Findings

Categories effectively model knowledge domains.

Categorical constructs can define and evaluate analogies.

Framework demonstrates analogy between solar system and hydrogen atom.

Abstract

In order to behave intelligently both humans and machines have to represent their knowledge adequately for how it is used. Humans often use analogies to transfer their knowledge to new domains, or help others with this transfer via explanations. Hence, an important question is: What representation can be used to construct, find, and evaluate analogies? In this paper, we study features of a domain that are important for constructing analogies. We do so by formalizing knowledge domains as categories. We use the well-known example of the analogy between the solar system and the hydrogen atom to demonstrate how to construct domain categories. We also show how functors, pullbacks, and pushouts can be used to define an analogy, describe its core and a corresponding blend of the underlying domains.