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 studies analogical proportions between booleans of the form `$a$ is to $b$ what $c$ is to $d$' called boolean proportions. Technically, we instantiate an abstract algebraic framework of analogical proportions -- recently introduced by the author -- in the boolean domain consisting of the truth values true and false together with boolean functions. It turns out that our notion of boolean proportions has appealing mathematical properties and that it coincides with a prominent model of boolean proportions in the general case. In a broader sense, this paper is a further step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.
翻译：模拟分析是人类智慧和创造力的核心,其应用包括常识推理、学习、语言获取和故事讲述等多种任务。本文研究“a美元”形式的布尔人之间的类似比例,即“a美元”形式的美元等于美元,即“d$”的美元,在技术上,我们从作者最近引进的模拟比例抽象代数框架,在布林域,包括真实和虚假的真理价值以及布林函数。结果显示,我们的布林比值概念具有吸引人的数学特性,它与一般情况下显著的布林比值模式相吻合。从广义上讲,本文是朝着模拟推理理论和学习系统迈出的又一步,有可能适用于基本AI问题,如常识推理和计算学及创造性。
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