认知中量子结构的实验证据
Experimental Evidence for Quantum Structure in Cognition
摘要：
我们证明了一个定理，该定理表明，一个集合的实验数据的隶属度权重的项目相对于一对概念和它的连接不能在一个经典的测量理论的权重结构中建模的情况下，实验数据包含的效果被称为过度延伸。由于过度延伸的效果，类似于众所周知的孔雀鱼效应的概念组合，是丰富的在所有的实验测试项目的权重相对于对的概念和它们的连接，我们的定理构成了一个不去定理的经典测量结构的共同数据的项目的成员权重相对于概念和它们的组合。我们提出了一个简单的几何准则，揭示了非经典的隶属度权重结构，并使用实验测量的隶属度权重估计的主题在实验中来说明我们的几何准则。对经典权结构的破坏类似于对量子力学中研究的著名的贝尔不等式的破坏，因此表明量子形式主义和量子隶属权的建模可以完成经典隶属权不能做的事情。
英文摘要：
We proof a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights can accomplish what classical membership weights cannot do.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
