Analogical proportions

Abstract Analogy-making is at the core of human and artificial intelligence creativity with applications to such diverse tasks as proving mathematical theorems building theories, common sense reasoning, learning, language acquisition, story telling. This paper introduces from first principles an abstract algebraic framework analogical proportions form ‘ a b what c d ’ in general setting universal algebra. enables us compare objects possibly across different domains uniform way which crucial for AI-systems. It turns out that our notion has appealing properties. As we construct model using only elementary concepts algebra, since questions some basic properties presupposed literature, convince reader plausibility show it can be naturally embedded into first-order logic via model-theoretic types prove perspective are compatible structure-preserving mappings. provides conceptual evidence its applicability. In broader sense, this step towards theory reasoning learning systems potential fundamental AI-problems like computational creativity.