Boolean connectives: probing the interplay between Language & Logic

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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.