Bilingual analogical proportions
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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 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 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.
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