Abstract
The paper explores the cognitive mechanisms involved in the verification of sentences with proportional quantifiers (e.g. “More than half of the dots are blue”). The first study shows that the verification of proportional sentences is more demanding than the verification of sentences such as: “There are seven blue and eight yellow dots”. The second study reveals that both types of sentences are correlated with memory storage, however, only proportional sentences are associated with the cognitive control. This result suggests that the cognitive mechanism underlying the verification of proportional quantifiers is crucially related to the integration process, in which an individual has to compare in memory the cardinalities of two sets. In the third study we find that the numerical distance between two cardinalities that must be compared significantly influences the verification time and accuracy. The results of our studies are discussed in the broader context of processing complex sentences.
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Notes
Chomsky (1957, 1969) famously proposed a mathematical model of formal grammars to talk about the complexity of the syntactic constructions. His complexity hierarchy classifies grammatical constructions into regular, context-free, context-sensitive, and recursively enumerable. The higher the construction in the hierarchy, the more difficult it is, especially if it potentially engages WM more. The computational model of quantifier verification has been formulated in terms of automata-theory that exactly corresponds to the Chomsky hierarchy: finite-automata recognize regular languages, PDAs recognize context-free languages, linear-bounded non-deterministic Turing machines correspond to the context-sensitive languages, and finally the class of enumerable languages is recognizable by Turing machines (see, e.g., Hopcroft et al. 2006).
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Acknowledgments
The work of the first author was supported by a Grant No. 2011/01/D/HS6/01920 funded by the National Science Centre in Poland. The second author would like to acknowledge a generous support of NWO Veni Grant 639.021.232.
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Zajenkowski, M., Szymanik, J. & Garraffa, M. Working Memory Mechanism in Proportional Quantifier Verification. J Psycholinguist Res 43, 839–853 (2014). https://doi.org/10.1007/s10936-013-9281-3
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DOI: https://doi.org/10.1007/s10936-013-9281-3