The purpose of this paper is to present a 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：本文旨在提出一种通过类比推理实现符号学习的新思路。为此，我们引入逻辑程序之间的有向类比关系，形如“$P$ 转化为 $Q$ 等价于 $R$ 转化为 $S$”，作为通过类比生成相似程序的机制。其核心思想是将近期提出的抽象代数类比框架中的片段实例化到逻辑程序设计领域。技术上，我们通过模块化定义类比关系，从“已知”源域中提取具体程序的抽象形式，并在“未知”目标域中实例化以获得类比程序。为此，我们引入了句法逻辑程序组合与拼接的代数运算。值得注意的是，本文揭示了模块化、泛化与类比之间的密切关联，我们认为这一关联值得未来深入探索。从更广泛的意义上讲，本文是对基于逻辑的类比推理与学习数学理论的进一步推进，有望应用于常识推理、计算学习与创造力等开放式人工智能问题。