Comprehension of Simple Quantifiers: Empirical Evaluation of a Computational Model

Abstract

We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality. In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves upon, the hypotheses and explanatory power of recent neuroimaging studies as well as provides evidence for the claim that human linguistic abilities are constrained by computational complexity.

Quantifiers and Working Memory

“…Subjects performed better on numerical quantifiers with low ranks than on the other determiners, and finally there were no differences between parity quantifiers and numerical quantifiers of high rank. The results support our predictions and are consistent with the previous findings in [3] and [17].…”

“…We created situations similar to the span task to compare numerical quantifiers of low and high rank, parity quantifiers and proportional quantifiers. The results enrich and support the data obtained previously in [1][2][3] and predictions drawn from a computational model [4,5]. …”

“…Among others, the results indicate that the numerical and parity quantifiers are processed faster than the proportional quantifiers. This is consistent with computational analysis as only proportional quantifiers demand a recognition mechanism with unbounded internal memory, like a stack in push-down automata (see [3]). Therefore, there is not only a quantitative but also qualitative difference between memory resources which are necessary to compute these two types of quantifiers.…”

“…We predicted that when subjects are asked to maintain arbitrary information in short-term memory then similar differences between quantifiers should be revealed as those described in [3] as well as in [16]. In particular, the difficulty (indicated by reaction time and accuracy) should decrease as follows: proportional quantifiers, numerical quantifiers of high rank, parity quantifiers, numerical quantifiers of low rank.…”

“…Cognitive difficulty of quantifier processing might be better assessed on the basis of complexity of the minimal corresponding automata [4,5]. Taking this perspective, in [3] an analogical reaction time experiment carefully differentiating between the following classes of quantifiers has been conducted (see Table 1). The study has shown that the increase in reaction time is determined by the minimal automata corresponding to the quantifier.…”