发表机构
Tel Aviv University（特拉维夫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于操作的概念数学评估框架，识别十三种操作，分析十个框架的承诺差异，并通过分类实证表明数学承诺影响理论解释力，呼吁混合形式。
AI 中文摘要
概念通常被定义为知识的抽象、紧凑表示，并被视作智能行为的基本单元。然而，认知科学、心理学和人工智能领域缺乏一种共享的数学语言来描述它们。现代系统将概念表示为向量、分布、符号、图以及其他结构，但这些形式通常被视为相互竞争，而非对共同问题的解决方案。我们提出一种基于操作的观点，通过评估数学框架所支持的概念操作来评判它们，识别出在认知科学、心理学和人工智能中反复出现的十三种操作（包括相似性、组合、泛化和接地）。我们表明，十个框架体现了对概念作为自包含内容、关系结构或演化过程的不同承诺，而这些承诺决定了每个框架自然支持哪些操作。例如，基于向量的模型促进了分级相似性和泛化，但在显式组合方面存在困难，而符号模型支持组合，但泛化能力较差。在我们检验的框架中，没有一个能在不扩展的情况下自然支持所有操作。我们以分类任务作为案例研究，实证检验了这一观点，将九种理论在同一项目上操作化，并与人类判断进行比较。尽管解决的是相同的概念问题，这些理论产生了不同的程序和结果，表明数学承诺塑造了理论所能解释的内容。我们呼吁采用混合形式，将内容、关系和过程视为共同的首要因素。
英文摘要
Concepts are commonly defined as abstract, compact representations of knowledge and treated as basic units of intelligent behavior. Yet, cognition, psychology, and AI lack a shared mathematical language for them. Modern systems represent concepts as vectors, distributions, symbols, graphs, and other structures, but these formalisms are typically treated as competing rather than as solutions to a common problem. We propose an operation-based view that evaluates mathematical frameworks by the conceptual operations they support, identifying thirteen operations (including similarity, composition, generalization, and grounding) that recur across cognition, psychology, and AI. We show that ten frameworks embody distinct commitments to concepts as self-contained content, relational structure, or evolving process, and that these commitments determine which operations each supports naturally. For example, vector-based models facilitate graded similarity and generalization but struggle with explicit composition, whereas symbolic models support composition but offer but generalize poorly. No single framework we examined naturally supports all operations without extension. We test this account empirically using categorization as a case study, operationalizing nine theories on the same items against human judgments. Despite addressing the same conceptual question, the theories produce different procedures and results, demonstrating that mathematical commitment shapes what a theory can explain. We call for hybrid formalisms that treat content, relation, and process as jointly primary.
