论文标题
类比比例
Analogical proportions
论文作者
论文摘要
类比制作是人类和人工智能和创造力的核心，以及在证明数学定理和构建数学理论，常识推理，学习，语言获取和故事讲述等各种任务中的应用。本文介绍了第一个原理在环球代数的一般环境中，形式为$ a $ a $的类似比例的抽象代数框架是$ b $ to $ d $。这使我们能够以统一的方式比较可能跨不同领域的数学对象，这对于AI系统至关重要。事实证明，我们的类似比例概念具有吸引人的数学特性。 As we construct our model from first principles using only elementary concepts of universal algebra, and since our model questions some basic properties of analogical proportions presupposed in the literature, to convince the reader of the plausibility of our model we show that it can be naturally embedded into first-order logic via model-theoretic types and prove from that perspective that analogical proportions are compatible with structure-preserving mappings.这为其适用性提供了概念证据。从广义上讲，本文是迈向类似推理和学习系统理论的第一步，该理论具有潜在的应用程序，可用于基本的AI问题，例如常识推理，计算学习和创造力。
Analogy-making is at the core of human and artificial intelligence and creativity with applications to such diverse tasks as proving mathematical theorems and building mathematical theories, common sense reasoning, learning, language acquisition, and story telling. This paper introduces from first principles an abstract algebraic framework of analogical proportions of the form `$a$ is to $b$ what $c$ is to $d$' in the general setting of universal algebra. This enables us to compare mathematical objects possibly across different domains in a uniform way which is crucial for AI-systems. It turns out that our notion of analogical proportions has appealing mathematical properties. As we construct our model from first principles using only elementary concepts of universal algebra, and since our model questions some basic properties of analogical proportions presupposed in the literature, to convince the reader of the plausibility of our model we show that it can be naturally embedded into first-order logic via model-theoretic types and prove from that perspective that analogical proportions are compatible with structure-preserving mappings. This provides conceptual evidence for its applicability. In a broader sense, this paper is a first step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like common sense reasoning and computational learning and creativity.
