Bilingual analogical proportions via hedges

• URL: http://arxiv.org/abs/2305.05614v2
• Date: Fri, 12 Jan 2024 10:15:07 GMT
• Title: Bilingual analogical proportions via hedges
• Authors: Christian Anti\'c
• Abstract summary: Analogical proportions are expressions of the form $a$ is to $b$ what $c$ is to $d$'' at the core of analogical reasoning. The purpose of this paper is to generalize his unilingual framework to a bilingual one where the underlying languages may differ.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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