Centre National de la Recherche Scientifique, Institut Jean-Nicod, Paris, FranceCentre National de la Recherche Scientifique, Institut des Sciences Cognitives, Lyon, FranceUniversité Lyon II, France.
Cogn Sci. 2006 Jul 8;30(4):691-723. doi: 10.1207/s15516709cog0000_75.
We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. We hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people's assessment of how well each of the 5 diagrams expresses the meaning of each of the quantified sentences. We report the results from 3 experiments using Gergonne's (1817) circles or an adaptation of Leibniz (1903/1988) lines as external representations and show them to support the predictions.
我们提出了一个经典量化句子（所有 P 是 Q，有些 P 是 Q，有些 P 不是 Q，以及没有 P 是 Q）的心理表象的集合论模型。我们将包含、排除及其否定作为基本概念。我们表明，尽管这些句子具有以杰根恩圆形式构成的语义表示的图式表达，但这些概念也可以以代数公式的形式在句法上表达。我们假设量化句子具有一种抽象的基础表示形式，这种形式对于公式及其相关的图表（模型）集是共同的。我们对人们对每个图表表达每个量化句子的含义的好坏的评估得出了 9 个预测（3 个语义、2 个语用和 4 个混合）。我们报告了使用杰根恩圆（1817 年）或莱布尼茨（1903/1988 年）线的改编作为外部表示的 3 个实验的结果，并表明它们支持这些预测。
