\begin{abstract} 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 developing an algebraic framework for logic-based analogical reasoning and learning in the setting of logic programming. The main idea is to instantiate the framework of analogical proportions of the form $a:b::c:d$, recently introduced by the author, in the domain of logic programming. That is, in this paper we introduce and study logic program proportions of the form $P:Q::R:S$ as a mechanism for learning similar programs by analogy-making. 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. 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 an algebraic theory of logic-based analogical reasoning and learning with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.

翻译：\ begin{ amptract} 分析学是人类智慧和创造力的核心,它应用到常识推理、学习、语言获取和故事叙事等多种任务。本文件通过在逻辑编程中开发基于逻辑的模拟推理和学习的代数框架,为人造一般情报的基础作出贡献。主要想法是即时化表格“$a:b:b:c:d$”的模拟比例框架,这是作者最近在逻辑编程领域引入的。这就是,在本文中,我们引入并研究“USP:Q:R:S$”的逻辑方案比例,作为通过类推学学习类似程序的机制。在技术上,我们从一个“已知”源域中产生具体方案的抽象形式,然后在“未知”目标域中即刻录,以获得类似的程序。有趣的是,我们的工作表明模块化、概括化和类推法之间的密切关系,我们认为今后应该进一步探讨。从广义上讲,这份文件是学习“IMB”推理学的更深层次和推理学。