The purpose of this paper is to present a {\em fresh} idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as $R$ transforms into $S$" as a mechanism for deriving similar programs by analogy-making. The idea is to instantiate a fragment of a recently introduced abstract algebraic framework of analogical proportions in the domain of logic programming. Technically, we define proportions in terms of modularity where we derive abstract forms of concrete programs from a "known" source domain which can then be instantiated in an "unknown" target domain to obtain analogous programs. To this end, we introduce algebraic operations for syntactic logic program composition and concatenation. Interestingly, our work suggests a close relationship between modularity, generalization, and analogy which we believe should be explored further in the future. In a broader sense, this paper is a further step towards a mathematical theory of logic-based analogical reasoning and learning with potential applications to open AI-problems like commonsense reasoning and computational learning and creativity.

翻译：本文旨在提出一种新的思想，即如何通过类比推理实现符号学习。为此，我们引入了逻辑程序之间的有向类比比例，形式为"$P$转换为$Q$等价于$R$转换为$S$"，作为通过类比生成相似程序的机制。其核心思想是在逻辑程序设计领域中实例化最近提出的抽象代数类比比例框架的一个片段。技术上，我们以模块性为基础定义比例，从"已知"源域中推导出具体程序的抽象形式，然后将其实例化到"未知"目标域中，以获得类比程序。为此，我们引入了句法逻辑程序组合与拼接的代数操作。有趣的是，我们的工作揭示了模块性、泛化与类比之间的紧密联系，我们认为这一关系应在未来进一步探索。从更广义的角度看，本文是迈向基于逻辑的类比推理与学习的数学理论的关键一步，其在常识推理、计算学习与创造力等开放AI问题上具有潜在应用价值。