[论文解读] Logic-Based Analogical Reasoning and Learning

Christian Antić|arXiv (Cornell University)|Sep 26, 2018

Logic, programming, and type systems被引用 1

一句话总结

本文提出了一种基于代数的逻辑程序化类比推理与学习框架，通过模块化和程序组合来建模类比。该框架能够从已知的源领域推导出未知目标领域的类比程序，为人工智能推理与学习建立语法相似性的基础。

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 abstract algebraic framework for logic-based analogical reasoning and learning in the setting of logic programming. The main idea is to define analogy in terms of modularity and to 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 program composition and concatenation and illustrate, by giving numerous examples, that programs have nice decompositions. Moreover, we show how composition gives rise to a qualitative notion of syntactic program similarity. We then argue that reasoning and learning by analogy is the task of solving analogical proportions between logic 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 first step towards an algebraic and mainly syntactic theory of logic-based analogical reasoning and learning in knowledge representation and reasoning systems, with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.

研究动机与目标

• 为逻辑程序中的类比推理建立正式的代数基础。
• 通过源域与目标域之间的程序组合与实例化来建模类比。
• 探讨模块化、泛化与类比在人工智能系统中的关系。
• 通过类比程序变换实现基于逻辑的学习与推理。
• 为知识表示与推理系统中的语法类比推理奠定基础。

提出的方法

• 通过代数运算定义类比，基于模块化与语法程序组合。
• 引入程序连接与组合作为构建与分解逻辑程序的核心操作。
• 利用组合产生的语法相似性来量化程序的相似程度。
• 应用类比比例求解逻辑程序之间的推理与学习任务。
• 通过实例化已知源领域的抽象形式，推导出目标领域的程序。
• 建立一种定性、以语法为导向的逻辑程序类比推理方法。

实验结果

研究问题

• RQ1 如何通过代数与语法规则正式定义逻辑程序中的类比？
• RQ2 模块化在实现类比推理与程序泛化中扮演何种角色？
• RQ3 如何将源领域的抽象程序形式实例化到目标领域，以生成类比程序？
• RQ4 程序组合、语法相似性与类比推理之间的关系是什么？
• RQ5 该框架如何支持人工智能系统中的学习与推理，特别是在常识推理与创造性思维方面？

主要发现

• 逻辑程序中的类比通过程序组合与连接的代数运算正式化。
• 程序具有天然的分解结构，支持模块化与可重用的类比推理。
• 语法相似性通过组合定性地浮现，为类比比较提供基础。
• 该框架揭示了模块化、泛化与类比在基于逻辑的人工智能中的深层联系。
• 类比推理与学习被重新表述为求解逻辑程序之间的类比比例。
• 该方法为类比推理提供了一套语法化、代数化的理论，具有在常识推理与计算创造力中应用的潜力。