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[2505.19792] Types of Relations: Defining Analogies with Category Theory
Summary
This paper explores the representation of knowledge through analogies using category theory, highlighting how features of domains can facilitate analogy construction.
Why It Matters
Understanding how to represent knowledge through analogies is crucial for both human cognition and artificial intelligence. This research provides a formal framework for constructing and evaluating analogies, which can enhance machine learning models and improve knowledge transfer across domains.
Key Takeaways
- Analogies play a vital role in knowledge transfer for humans and machines.
- The paper formalizes knowledge domains as categories to aid analogy construction.
- Key concepts such as functors, pullbacks, and pushouts are utilized to define analogies.
- The analogy between the solar system and hydrogen atom serves as a practical example.
- This framework can enhance AI's ability to learn and adapt across different domains.
Computer Science > Artificial Intelligence arXiv:2505.19792 (cs) [Submitted on 26 May 2025 (v1), last revised 26 Feb 2026 (this version, v2)] Title:Types of Relations: Defining Analogies with Category Theory Authors:Claire Ott, Frank Jäkel View a PDF of the paper titled Types of Relations: Defining Analogies with Category Theory, by Claire Ott and 1 other authors View PDF 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. Comments: Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2505.19792 [cs.AI] (or arXiv:2505.19792v2 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2505.19792 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Claire Ott [view email] [v1] Mon, 26 May 2025 10:22:44...
