Bilingual analogical proportions via hedges
This work is an incremental step towards a mathematical theory of analogical reasoning, relevant for researchers in AI and logic.
The paper tackles the problem of extending an existing unilingual framework for analogical proportions to a bilingual setting where source and target languages may differ, using hedges in justifications to achieve a major generalization that vastly extends the framework's applicability.
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.