Logic across languages: Expressing and interpreting connectives cross-linguistically

逻辑连接词是人类形式化思维的基石之一，与数字和几何一样。170年前，英国逻辑学家布尔提出了布尔逻辑，认为‘or’对应于‘|’运算符，而‘and’对应于‘&’运算符。布尔逻辑在数学、计算机科学和其他领域无处不在，尽管布尔的目标从来不是提供证据，证明AND和/或真的是思维的原语。后来的许多形式语言学著作由于是从欧洲中心的角度进行研究而产生了偏见，在欧洲中心的观点中，自然语言和逻辑之间的映射是欺骗性的直接映射。然而，有理由对布尔图景提出质疑。例如，布尔定律告诉我们，一旦我们在系统中有了否定，我们只需要两个连接词中的一个来派生另一个，所以我们可能只期望连词或析取词是一个原语，但这并没有在经过充分研究的欧洲语言中得到证实。与印欧语言不同，到目前为止，还没有深入的跨语言研究，不仅记录了一种语言可能表达并列的所有不同方式，而且还描述了这些结构之间在语义和形态句法分布方面的差异。人们会认为，检测一种语言如何表达像And和Or这样的基本概念应该是相当微不足道的，但有些语言完全缺乏连接词，即它们没有单一的语素可以可靠地翻译为和跨越所有上下文。事实证明，这样的语言循环使用析取来表达合取意义(例如Warlpiri，美国手语)。另一方面，在一些语言中，表达析取涉及到在该语言中表达连接的其他用法的诉求(例如，夏延语中的析取是建立在合取成分之上的)。这个项目是对自然语言和布尔逻辑之间匹配和不匹配的正式研究的第一个重要贡献，因为它是以强大的跨语言调查为基础的。框架的发展使我们能够概念化形成合取和析取意义的策略以及这些策略可能变化的维度，这使得这个项目非常及时。我们将从以下三个方面进行研究：(I)连接词和否定词之间的相互作用，以及识别布尔连接词的预测解释与实际自然语言解释之间的不匹配；(Ii)复杂连接词相对于单纯连接词的功能；(Iii)连接词的多功能性程度。

Logical connectives are one of the building blocks of human formal thought along with number and geometry. 170 years ago the British logician Boole formulated Boolean logic, arguing that ‘or’ corresponds to the ‘|’ operator and that ‘and’ corresponds to the ‘&’ operator. Boolean logic is ubiquitous in math, computer science and other fields, even though Boole’s goal was never to provide evidence that and and or really are primitives of thought. Much of the later formal linguistic work has been biased by virtue of being stud- ied from a Eurocentric perspective, where the mapping between natural language and logic is deceptively straightforward. Yet there are reasons to question the Boolean picture. For example, Boolean laws tell us that once we have negation in the system we only need one of the two connectives to derive the other, so we might expect only conjunction, or only disjunction, to be a primitive, and yet that has not been borne out in the well-studied languages of Europe.Moving away from the Indo-European languages, to date, no in-depth cross-linguistic study has been con- ducted that not only documents all the different ways a single language may express coordination, but also describes the differences among these constructions with respect to their semantic and morphosyntactic distribution. One would expect that it should be pretty trivial to detect how a language expresses concepts as basic as and and or, yet there are languages that lack conjunction altogether, i.e. they have no single morpheme that can be reliably translated as and across all contexts. Such languages, as it turns out, recycle disjunction to express conjunctive meanings (e.g. Warlpiri, American Sign Language). On the flip side, there are languages where expressing disjunction involves an appeal to what is otherwise used to express conjunc- tion in that language (e.g. Cheyenne where disjunction is built off of the conjunctive element). This project constitutes the first serious contribution to this formal study of the matches and mismatches between natural language and Boolean logic, as it is underpinned by a strong cross-linguistic investigation. The develop- ment of frameworks that enable us to conceptualize the strategies for forming conjunctive and disjunctive meanings and the dimensions along which such strategies may vary is fairly recent, making this project well timed. The three main ways we will proceed with this investigation are the following: (i) interaction between connectives and negation and identifying mismatches between the predicted interpretation of the Boolean connective and the actual natural language interpretation, (ii) the function of complex connectives as opposed to simplex connectives, and (iii) the extent of the poly-functionality of connectives.