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This paper studies analogical proportions in monounary algebras consisting only of a universe and a single unary function, where we analyze the role of congruences, and 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.
期刊介绍：
Annals of Mathematics and Artificial Intelligence presents a range of topics of concern to scholars applying quantitative, combinatorial, logical, algebraic and algorithmic methods to diverse areas of Artificial Intelligence, from decision support, automated deduction, and reasoning, to knowledge-based systems, machine learning, computer vision, robotics and planning.
The journal features collections of papers appearing either in volumes (400 pages) or in separate issues (100-300 pages), which focus on one topic and have one or more guest editors.
Annals of Mathematics and Artificial Intelligence hopes to influence the spawning of new areas of applied mathematics and strengthen the scientific underpinnings of Artificial Intelligence.
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