Recognition confusions among quantifiers

Questions About Quantifiers: Symbolic and Nonsymbolic Quantity Processing by the Brain

One approach to understanding how the human cognitive system stores and operates with quantifiers such as "some," "many," and "all" is to investigate their interaction with the cognitive mechanisms for estimating and comparing quantities from perceptual input (i.e., nonsymbolic quantities). While a potential link between quantifier processing and nonsymbolic quantity processing has been considered in the past, it has never been discussed extensively. Simultaneously, there is a long line of research within the field of numerical cognition on the relationship between processing exact number symbols (such as "3" or "three") and nonsymbolic quantity. This accumulated knowledge can potentially be harvested for research on quantifiers since quantifiers and number symbols are two different ways of referring to quantity information symbolically. The goal of the present review is to survey the research on the relationship between quantifiers and nonsymbolic quantity processing mechanisms and provide a set of research directions and specific questions for the investigation of quantifier processing.

Probing the mental representation of quantifiers

In this study, we investigate the mental representation of non-numerical quantifiers ("some", "many", "all", etc.) by comparing their use in abstract and in grounded perceptual contexts. Using an approach similar to that used in the number domain, we test whether (and to what extent) such representation is constrained by the way we perceive the world through our senses. In two experiments, subjects either judged the similarity of quantifier pairs (presented as written words) or chose among a predetermined list of quantifiers the one that best described a visual image depicting a variable number of target and non-target items. The results were rather consistent across experiments, and indicated that quantifiers are mentally organized on an ordered but non-linear compressed scale where the quantifiers that imply small quantities appear more precisely differentiated across each other compared to those implying large quantities. This fits nicely with the idea that we construct our representations of such symbols mainly by mapping them to the representations of quantities that we derive from perception.

Response Options and Presentation Format as Contributors to Conditional Reasoning

The present study examines whether students’ inability to solve conditional reasoning problems, shown in previous studies, is at least partially attributable to having to choose among logically incorrect response options. In two experiments, students evaluated conclusions to conditional reasoning problems where one of several response options was either the standard, Sometimes true, or the more logically appropriate, Could be true. Decision accuracy was related to the logical appropriateness of the response options available. This relationship was replicated across different problem types and formats.

Spontaneous, modality-general abstraction of a ratio scale

The existence of a generalized magnitude system in the human mind and brain has been studied extensively but remains elusive because it has not been clearly defined. Here we show that one possibility is the representation of relative magnitudes via ratio calculations: ratios are a naturally dimensionless or abstract quantity that could qualify as a common currency for magnitudes measured on vastly different psychophysical scales and in different sensory modalities like size, number, duration, and loudness. In a series of demonstrations based on comparisons of item sequences, we demonstrate that subjects spontaneously use knowledge of inter-item ratios within and across sensory modalities and across magnitude domains to rate sequences as more or less similar on a sliding scale. Moreover, they rate ratio-preserved sequences as more similar to each other than sequences in which only ordinal relations are preserved, indicating that subjects are aware of differences in levels of relative-magnitude information preservation. The ubiquity of this ability across many different magnitude pairs, even those sharing no sensory information, suggests a highly general code that could qualify as a candidate for a generalized magnitude representation.

VR-MDS: multidimensional scaling for classification tasks of virtual and real stimuli

Evaluating the perceptual similarity between virtual and real sensory stimuli has been a serious problem for virtual reality interface researchers for a long time. One of the most commonly used evaluation methods is a classification task where assessors classify randomly presented stimuli into multiple candidate types. The results of this method are summarized using two types of confusion matrices, which have different stimulus sets. The present study developed a method that computes the locations of simulated and real stimuli in a perceptual space on the basis of the two confusion matrices. The spatial distribution of the stimuli allows us to visually interpret the perceptual relationships between stimuli and their perceptual dimensionality. This method is recommended when the guidance index based on the answer ratios of the confusion matrices is fairly high.

A review of human linguistic probability processing: General principles and empirical evidence

This article reviews research on how people use and understand linguistic expressions of uncertainty, with a view toward the needs of researchers and others interested in artificial intelligence systems. We discuss and present empirical results within an inductively developed theoretical framework consisting of two background assumptions and six principles describing the underlying cognitive processes.

Attentional focusing with quantifiers in production and comprehension

There is a very large number of quantifiers in English, so many that it seems impossible that the only information that they convey is about amounts. Building on the earlier work of Moxey and Sanford (1987), we report three experiments showing that positive and negative quantifiers focus on different subsets of the logical possibilities that quantifiers allow semantically. Experiments 1 and 2 feature a continuation task with quantifiers that span a full range of denotations (from near 0% to near 100%) and show that the effect is not restricted to quantifiers denoting small amounts. This enables a distinction to be made between generalization and complement set focus proper. The focus effects extend to comprehension, as shown by a self-paced reading study (Experiment 3). It is noted that the focus effects obtained are compatible with findings from earlier work by Just and Carpenter (1971), which used a verification paradigm, and in fact these effects constitute a direct test of inferences Just and Carpenter made about mechanisms of encoding negative quantifiers. A related but different explanation is put forward to explain the present data. The experiments show a quantifier function beyond the simple denotation of amount.