当前位置: X-MOL 学术arXiv.cs.SC › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Analogical Proportions
arXiv - CS - Symbolic Computation Pub Date : 2020-06-04 , DOI: arxiv-2006.02854
Christian Anti\'c

Analogy-making is at the core of human intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper contributes to the foundations of artificial general intelligence by introducing 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. The main idea is to define solutions to analogical equations in terms of generalizations and to derive abstract terms of concrete elements from a `known' source domain which can then be instantiated in an `unknown' target domain to obtain analogous elements. We extensively compare our framework with two prominent and recently introduced frameworks of analogical proportions from the literature in the concrete domains of sets, numbers, and words and show that our framework yields strictly more reasonable solutions in all of these cases which provides evidence for the applicability of our framework. In a broader sense, this paper is a first step towards an algebraic theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.

中文翻译:

类比比例

类比是人类智能和创造力的核心,可应用于常识推理、学习、语言习得和讲故事等各种任务。本文通过在通用代数的一般设置中引入一个抽象代数框架,形式为“$a$ 对 $b$ 什么是 $c$ 对 $d$”的类比比例,为人工智能的基础做出了贡献。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 AI 系统至关重要。主要思想是根据概括定义类比方程的解,并从“已知”源域中导出具体元素的抽象项,然后可以在“未知”目标域中实例化以获得类似元素。我们将我们的框架与集合、数字和单词的具体领域的文献中两个突出的和最近引入的类比框架进行了广泛的比较,并表明我们的框架在所有这些情况下都产生了更合理的解决方案,这为适用性提供了证据我们的框架。从更广泛的意义上讲,本文是类比推理和学习系统的代数理论的第一步,具有对基本人工智能问题(如常识推理、计算学习和创造力)的潜在应用。和文字,并表明我们的框架在所有这些情况下都能产生更合理的解决方案,这为我们的框架的适用性提供了证据。从更广泛的意义上讲,本文是类比推理和学习系统的代数理论的第一步,具有对基本人工智能问题(如常识推理、计算学习和创造力)的潜在应用。和文字,并表明我们的框架在所有这些情况下都能产生更合理的解决方案,这为我们的框架的适用性提供了证据。从更广泛的意义上讲,本文是类比推理和学习系统的代数理论的第一步,具有对基本人工智能问题(如常识推理、计算学习和创造力)的潜在应用。
更新日期:2020-08-26
down
wechat
bug