Analogical proportions in monounary algebras
Christian Anti\'c

TL;DR
This paper investigates how analogical proportions can be characterized within monounary algebras, specifically using the natural numbers and the successor function, revealing a relation based on difference proportions.
Contribution
It introduces a characterization of analogical proportions in monounary algebras, focusing on the infinite case with natural numbers and the successor function.
Findings
Analogical proportions are characterized by difference proportions in the natural numbers.
The study provides a formal relation for analogies in monounary algebras.
The approach applies to infinite monounary algebras with a unary function.
Abstract
This paper studies analogical proportions in monounary algebras consisting only of a universe and a single unary function. We show that the analogical proportion relation is characterized in the infinite monounary algebra formed by the natural numbers together with the successor function via difference proportions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Mathematical and Theoretical Analysis · Rings, Modules, and Algebras
