Boolean connectives: probing the interplay between Language & Logic

在过去的几十年里，关于语言对算术能力和早期数字学习的影响的研究一直在显著增长。但是，当我们转向数学认知的其他领域时，例如那些涉及可以用日常语言表达的基本逻辑概念的领域，关于语言影响的研究仍然缺乏。BooLL项目旨在填补这一空白，并为逻辑能力是否依赖于母语这一问题带来了新的方法和证据。我们专注于布尔连接NOT， OR， AND， XOR， NOR， NAND，并开发了一系列非语言任务来调查儿童和成人对这些连接词的理解，以及组成这些连接词的能力。一些布尔连接词可以在自然语言中表示为单个词汇项（NOR），而另一些则不能（*NAND）。我们的任务涉及两种连接词，并允许我们对它们进行比较。我们研究它们揭示了逻辑、自然语言语义和语用学，以及它们之间的相互作用。我们的实验范例专门针对逻辑和语言分歧的领域，例如逻辑连接词到自然语言连接词的清单和映射（例如，语言连接词“或”可以映射到包含或或排除异或），或者已知会导致标准逻辑和语言之间不匹配的语法方面。否定序列的否定和谐解释，歧义和跨语言差异如何解释否定和分离（“不是A或B”）或连接（“不是A和B”）的组合，语用丰富。非语言逻辑能力是用一个新的实验范式来评估的：一个电脑游戏（酷布尔学校游戏），作为我们项目准备的一部分，专门设计用于学习和测试布尔连接器。在软件中跟踪参与者的游戏过程，可以生成丰富的数据，显示母语不同的儿童和成人如何以及多快地解决涉及单个或组合布尔连接词的不同任务。语言理解是评估与一个新开发的测试工具：数学字题涉及布尔连接词。尽管在心理语言学文献中对自然语言中逻辑算子的组合解释进行了丰富的探究传统，但据我们所知，在非语言语境中（即语言领域之外）没有对逻辑算子的组合解释进行实验研究。因此，BooLL寻求通过采取第一步探索独立于语言的逻辑组合能力来开辟新天地。

Research on the impact of language on arithmetic ability and early numerical learning has been growing significantly over the last decades. But when we turn to other areas of mathematical cognition, such as those involving basic logical concepts that can be expressed using everyday language, research on the impact of language is still lacking. The BooLL project seeks to fill this gap and brings novel methodology and evidence to bear on the issue of whether logical abilities are dependent on native language. We focus on the Boolean connectors NOT, OR, AND, XOR, NOR, NAND and develop a battery of nonverbal tasks to investigate the understanding of such connectives both by children and by adults, as well as the ability to compose these connectives. Some Boolean connectives can be expressed in natural language as a single vocabulary item (NOR), while others cannot (*NAND). Our tasks involve both kinds of connectives and allow us to compare them. We investigate what they reveal about logic, natural language semantics and pragmatics, and their interactions. Our experimental paradigms specifically target areas where logic and language diverge, such as the inventory and mapping of logical connectives to natural language connectives (e.g. the linguistic connective 'or' can map on to either inclusive OR or exclusive XOR), or aspects of the grammar that are known to cause a mismatch between standard logic and language: negative concord construals of sequences of negation, ambiguities and cross linguistic variation in how combinations of negation and disjunction ('not A or B') or conjunction ('not A and B') are interpreted, pragmatic enrichment. Nonverbal logical abilities are assessed with a new experimental paradigm: a computer game (the Cool Boole School Game) professionally designed as part of our project preparation for the purpose of learning and testing Boolean connectors. Tracking participants’ game-play in the software creates rich data on how and how quickly children and adults with different native languages are able to solve different tasks involving single or combinations of Boolean connectives. Verbal comprehension is assessed with a newly developed test instrument: Mathematical Word Problems involving Boolean connectives. Although there is a rich tradition of inquiry in the psycholinguistics literature on the compositional interpretation of logical operators in natural language, there is to our knowledge no experimental research on the compositional interpretation of logical operators in nonverbal contexts – that is, outside the domain of language. BooLL thus seeks to break new ground by taking a first step towards probing compositional abilities in logic independently of language.