2023/05/02 by Christian Antić, Antić, Christian
Computer Science · #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2305.05614
openalex publication_date 2023/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Analogical proportions are expressions of the form ``a is to b what c is to d'' at the core of analogical reasoning which itself is at the core of human and artificial intelligence. The author has recently introduced \em from first principles an abstract algebro-logical framework of analogical proportions within the general setting of universal algebra and first-order logic. In that framework, the source and target algebras have the \em same underlying language. The purpose of this paper is to generalize his unilingual framework to a bilingual one where the underlying languages may differ. This is achieved by using hedges in justifications of proportions. The outcome is a major generalization vastly extending the applicability of the underlying framework. In a broader sense, this paper is a further step towards a mathematical theory of analogical reasoning.