Working Memory Mechanism in Proportional Quantifier Verification

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.

Measuring the cognitive cost of downward monotonicity by controlling for negative polarity

“…As shown in Figure 2 and presented in Table 3, an effect of Standard was also foundproportional comparison takes longer than cardinal comparison. This effect can be explained by additional working memory resources required to process proportions, as corroborated by experimental data on quantifiers Zajenkowski, Szymanik & Garraffa 2014). We did not find the effect of Standard to be affected by Type.…”

Processing of Numerical and Proportional Quantifiers

“…It was shown that proportional quantifiers led to a similar effect, despite the use of a much larger total number of 50 circles with varying proportions between yellow and blue circles (Heim et al, 2012). Zajenkowski et al (2014) reported distance effects, when evaluating sentences with "more than half" from the computational perspective of quantifier verification. The presence of distance effects even in case of counting suggests that the integration of numerical information required for comparing two numerosities may lead to these effects.…”

“…Results obtained in their investigations followed their predictions. Poor performance was observed on proportional quantifiers (more than half) as compared to other quantifier types, in healthy adults (Szymanik & Zajenkowski, 2010;Zajenkowski et al, 2014) as well as in patients with cortico-basal degeneration (CBD), fronto-temporal dementia (FTD), Alzheimer's disease (McMillan et al, 2005(McMillan et al, , 2006Troiani, Clark, & Grossman, 2011), and schizophrenia (Zajenkowski et al, 2011). On the one hand, the deficits observed in patients with CBD and FTD were attributed to the underlying numerical impairments, while quantifier impairments in patients with schizophrenia were attributed to their problems with executive functioning, mainly working memory as well as language impairments.…”

“…The mapping of quantifiers onto numerical scales has been proposed in logic, formal semantics, syllogistic reasoning as well as linguistic comprehension and processing (Bass, Cascio, & O'Connor, 1974;Clark, 1969;Geurts, 2003;Holyoak & Glass, 1978;Sanford, Moxey, & Paterson, 1994). 1 However, the direct link between magnitude knowledge and quantifier comprehension was established in cognitive neuroscience more recently (Halberda, Taing, & Lidz, 2008a;Heim et al, 2012;Lidz, Pietroski, Halberda, & Hunter, 2011;McMillan, Clark, Moore, Devita, & Grossman, 2005;McMillan, Clark, Moore, & Grossman, 2006;Odic, Pietroski, Hunter, Lidz, & Halberda, 2013;Pietroski, Lidz, Hunter, & Halberda, 2009;Szymanik & Zajenkowski, 2010;Troiani et al, 2009;Zajenkowski, Styla, & Szymanik, 2011;Zajenkowski, Szymanik, & Garraffa, 2014). Moreover, the exact role of numerical processing in interpreting quantifiers, namely, in estimation and comparison, is gradually emerging (Halberda et al, 2008a;Heim et al, 2012;Lidz et al, 2011;Odic et al, 2013;Pietroski et al, 2009;Zajenkowski et al, 2014).…”

“Few” or “Many”? An Adaptation Level Theory Account for Flexibility in Quantifier Processing

“…The objective of the present study was to bridge the gap between this theory in the sensory-perceptual domain and the linguistic-semantic domain, which relies on similar perception processes but requires additional cognitive evaluations to map one representation onto the other (e.g., Halberda et al, 2008;Pietroski et al, 2009;Zajenkowski, 2009, 2010;Lidz et al, 2011;Zajenkowski et al, 2011Zajenkowski et al, , 2014Heim et al, 2012;Cheng et al, 2013;Odic et al, 2013;Zajenkowski and Szymanik, 2013). The crucial difference between the sensoryperceptual scenario and the linguistic-semantic experiment lies in the explicitness of the manipulation: Whereas sensory adaptation level shifts "happen" because of the exposure to varying degrees of stimulus intensities, the degree shift in the quantifier experiments (Heim et al, 2015(Heim et al, , 2016 was (at least partly) introduced by explicit reinforcement learning.…”