Analogical proportions in monounary algebras
This work addresses a theoretical problem in abstract algebra for researchers in mathematical logic and formal methods, but it appears incremental as it focuses on a specific algebraic structure.
The paper tackled the problem of characterizing analogical proportions in monounary algebras, specifically showing that in the infinite monounary algebra of natural numbers with the successor function, the relation is characterized via difference proportions.
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.