Baratgin Jean, Politzer Guy, Over David E, Takahashi Tatsuji
CHArt (P-A-R-I-S), Université Paris 8 & EPHE, Paris, France.
Institut Jean Nicod, École Normale Supérieure, Paris, France.
Front Psychol. 2018 Sep 4;9:1479. doi: 10.3389/fpsyg.2018.01479. eCollection 2018.
Psychological research on people's understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional which was often evaluated as true when and are true, false when is true and is false but irrelevant" (devoid of value) when is false (whatever the value of ). This was called the "psychological defective table of the conditional." Here we show that far from being anomalous the "defective" table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants' truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people's interpretations of natural language connectives. We find that de Finetti's (1936/1995) three-valued system is the best approximation to participants' truth tables.
传统上，关于人们对自然语言连接词理解的心理学研究使用真值表任务，即参与者在命题逻辑框架内，根据复合句各组成部分的真假来评估该复合句的真假。一个令人困惑的结果涉及指示性条件句，当条件句的前件和后件都为真时，该条件句常被评估为真；当前件为真而后件为假时，该条件句被评估为假；但当前件为假时（无论后件的值是什么），该条件句被评估为“无关”（无真值）。这被称为“条件句的心理缺陷真值表”。在此我们表明，“缺陷”真值表模式远非异常，它揭示了自然语言基本连接词在三值框架下的连贯语义。这是通过在向参与者呈现肯定为真、肯定为假或既非真也非假的陈述时，建立他们对否定、合取、析取、条件句和双条件句的真值表来实现的。我们回顾了来自逻辑学、语言学、量子力学基础、哲学逻辑和人工智能的三值真值表系统，以查看这些系统中的哪一个能充分描述人们对自然语言连接词的解释。我们发现德·菲内蒂（1936/1995）的三值系统最接近参与者的真值表。
