Improving methodology of quantifier comprehension experiments

Jakub Szymanik, Marcin Zajenkowski
2009 Neuropsychologia  
Introduction Recently, research devoted to computational modeling of quantifier comprehension has been extensively published in this journal. McMillan et al. (2005) using neuroimaging methods examined the pattern of neuroanatomical recruitment while subjects were judging the truth-value of statements containing natural language quantifiers. The authors were considering two standard types of quantifiers: first-order (e.g., "all", "some", "at least 3"), and higher-order quantifiers (e.g., "more
more » ... an half", "an even number of"). They presented the data showing that all quantifiers recruit the right inferior parietal cortex, which is associated with numerosity, but only higher-order quantifiers recruit the prefrontal cortex, which is associated with executive resources, like working memory. In the latest paper Troiani et al. (2009) assessed quantifier comprehension in patients with corticobasal degeneration (CBD) and healthy subjects. They compared numerical quantifiers, like "at least 3", which require magnitude processing, and logical quantifiers, like "some", which can be understood using a simple form of perceptual logic. Their findings are consistent with the claim that numerical quantifier comprehension depends on a lateral parietal-dorsolateral prefrontal network, but logical quantifier comprehension depends instead on a rostromedial prefrontal-posterior cingulate network. According to the authors of the mentioned studies, their results verify a particular computational model of natural language quantifier comprehension posited by linguists and logicians (see e. g., van Benthem, 1986). One of the authors of the present comment has challenged this statement by invoking differences -missed in (McMillan et al., 2005) -between logical (expressibility) and computational (working memory) properties of quantifiers (Szymanik, 2007). It was suggested that the distinction between first-order and higher-order quantifiers does not coincide with the computational resources required to compute the meaning of quantifiers. Cognitive difficulty of quantifier processing might be better assessed on the basis of complexity of the minimal corresponding automata. For example, both logical and numerical quantifiers are first-order. However, computational devices recognizing logical quantifiers have a fixed number of states while the number of states in automata corresponding to numerical quantifiers grows with the rank of the quantifier. This observation partially explains the differences in processing between those two types of quantifiers (Troiani et al. 2009) and links them to the computational model. Taking this
doi:10.1016/j.neuropsychologia.2009.04.004 pmid:19607955 fatcat:2baoempbt5a5venlhp5g2l776i