Semantic access in number processing investigated with Japanese Kanji and Kana numerals

In number processing, semantic representations are efficiently activated. These representations frequently affect task performance, as demonstrated by semantic effects such as the distance effect (longer reaction times to closer numerical pairs in comparison tasks). The objective of this study was to investigate whether efficient semantic access is a distinctive feature of number processing using the Japanese language. Japanese was chosen to investigate possible effects of ideographic processing and word frequency: Kanji numerals in Japanese are ideograms and are used frequently, while Kana numerals are phonograms and are used infrequently. The results confirmed a distance effect in the numerical and physical matching tasks with both Arabic and Kanji numerals regardless of notation or task (Experiment 1). However, the effect was not observed with the Kana pairs (Experiment 2), thereby suggesting that semantic access is not always efficient in number processing. The results can be explained coherently within a general framework of word recognition by assuming that both the type of character and the word frequency play a critical role in determining the efficiency of semantic access.     

The perception of number from the separability of the stimulus: The Stroop effect revisited

The literature on numerical perception is reviewed from the standpoint of research on selective attention, and predictions are made concerning the dimensional interaction between physical and numerical size of numerals. We manipulated stimulus differences to make the classification of numerical value slightly better (Experiment 1), substantially better (Experiment 2), or worse (Experiments 3–4) than classification of physical size. Garner, Stroop, and redundancy effects were used to gauge the degree of interactive processing. For nearly matched discriminability, both number and size appeared separable when the dimensions were varied orthogonally, but showed Stroop interference and redundancy gain when the dimensions were varied in a correlative fashion. When mismatched, asymmetric Garner and Stroop effects emerged in orthogonal contexts along with Stroop and redundancy gains in correlative contexts. These findings define a unique relation: Numerical value and physical size were optionally separable dimensions. We conclude that a magnitude representation is not mandatory for the perception of numerals. Our conclusions offer a new perspective for understanding both numerical perception and the Stroop phenomenon itself.     

Divided stimulus control: a replication and a quantitative model

Four pigeons were trained on a conditional discrimination. The conditional stimuli were compounds of pairs of stimuli from two different dimensions, fast versus slow cycles of red or green stimuli, and short- versus long-duration presentations of these cycles. Across conditions, the probability of reinforcers for correctly responding to each dimension was varied from 0 to 1. Discriminability, measured by log d, for stimuli on a dimension increased as the relative frequency of reinforcers for that dimension increased, replicating the results of Shahan and Podlesnik (2006). Two further conditions showed that discriminability between stimuli on each dimension was unaffected by whether the stimuli on the other dimension varied or were constant. Finally, maximal discriminability was unchanged in a redundant-relevant cues condition in which either of the stimuli comprising a compound signaled the same correct response. Davison and Nevin's (1999) model provided an excellent quantitative account of the effect of relative reinforcer frequency on discriminability, and thus of the way in which divided stimulus control is itself controlled by relative reinforcement.     

The prioritization of perceptual processing in categorization

In three experiments, the effects of selective attention on perceptual processes in a complex multidimensional object categorization task were investigated. In each experiment, participants completed a perceptual-matching task to gain estimates of the perceptual salience of each stimulus dimension, then a categorization task using the same stimuli. In Experiments 1 and 2, the perceptual processing of stimulus dimensions was faster when dimensions were more diagnostic of category membership, regardless of their perceptual salience. Experiment 3 demonstrated that this prioritization of perceptual processing was evident even when stimuli were presented in unpredictable locations during categorization, indicating that the physical characteristics of the stimulus guide selective attention to diagnostic stimulus dimensions.     

Event-related brain potentials and cognitive processes related to perceptual—motor information transmission

In the present study, event-related potentials (ERPs) were recorded to investigate cognitive processes related to the partial transmission of information from stimulus recognition to response preparation. Participants classified two-dimensional visual stimuli with dimensions size and form. One feature combination was designated as the go-target, whereas the other three feature combinations served as no-go distractors. Size discriminability was manipulated across three experimental conditions. N2c and P3a amplitudes were enhanced in response to those distractors that shared the feature from the faster dimension with the target. Moreover, N2c and P3a amplitudes showed a crossover effect: Size distractors evoked more pronounced ERPs under high size discriminability, but form distractors elicited enhanced ERPs under low size discriminability. These results suggest that partial perceptual—motor transmission of information is accompanied by acts of cognitive control and by shifts of attention between the sources of conflicting information. Selection negativity findings imply adaptive allocation of visual feature-based attention across the two stimulus dimensions.     

Rapid proportion comparison with spatial arrays of frequently used meaningful visual symbols

It has been shown that when two arrays of Arabic numerals were briefly presented, observers could accurately indicate which array contained the larger number of a target numeral. This study investigated whether this rapid proportion comparison can be extended to other meaningful symbols that share some of notable properties of Arabic numerals. We tested mainly several Japanese Kanji letters, each of which represents a meaning and can work as a word. Using physically identical stimulus sets that could be interpreted as different types of letters, Experiment 1 first confirmed the rapid proportion comparison with Arabic numerals for Japanese participants. Experiment 2 showed that the rapid proportion comparison can be extended to Kanji numerals. Experiment 3 successfully demonstrated that rapid proportion judgments can be found with non-quantitative Kanji letters that are used frequently. Experiment 4 further demonstrated the rapid proportion comparison with frequently used meaningful non-letter symbols (gender icons). The rapid processing cannot be attributed to fluent processing of familiar items, because it was not found with familiar phonograms (Japanese Kana letters). These findings suggest that the rapid proportion comparison can be commonly found with frequently used meaningful symbols, even though their meaning is not relevant to the task.     

Comparative judgments of symbolic and non-symbolic stimuli yield different patterns of reaction times

Are different magnitudes, such as Arabic numerals, length and area, processed by the same system? Answering this question can shed light on the building blocks of our mathematical abilities. A shared representation theory suggested that discriminability of all magnitudes complies with Weber's law. The current work examined this suggestion. We employed comparative judgment tasks to investigate different types of comparisons — conceptual comparison of numbers, physical comparison of numbers and physical comparison of different shapes. We used 8 different size ratios and plotted reaction time as a function of these ratios. Our findings suggest that the relationship between discriminability and size ratio is not always linear, as previously suggested; rather, it is modulated by the type of comparison and the type of stimuli. Hence, we suggest that the representation of magnitude is not as rigid as previously suggested; it changes as a function of task demands and familiarity with the compared stimuli.     

The effects of number of sample stimuli and number of choices in a detection task on measures of discriminability

Six pigeons were trained on a conditional discrimination task involving the discrimination of various intensities of yellow light. The research asked whether stimulus—response discriminability measures between any pair of stimuli would remain constant when a third or fourth sample and reinforced response were added. The numbers of different sample stimuli presented and different responses reinforced were two (Part 1), three (Parts 2 and 4), and four (Part 3). Across conditions within parts, the ratios of reinforcers obtainable for correct responses were varied over at least five levels. In Part 5, the numbers of sample stimuli and reinforced responses were varied among two, three, and four, and the reinforcer ratio between consecutive remaining samples was constant at 2:1. It was found that once a particular response had been reinforced, subjects continued to emit that response when the conditional stimulus for that response was no longer presented. Data analysis using a generalization-based detection model indicated that this model was able to describe the data effectively. Four findings were in accord with the theory. First, estimates of stimulus—response discriminability usually decreased as the arranged physical disparity between the sample stimuli decreased. Second, stimulus—response discriminability measures were independent of response—reinforcer discriminability measures, preserving parameter invariance between these measures. Third, stimulus—response discriminability measures for constant pairs of conditional stimuli did not change systematically as conditional stimulus—response alternatives were added. Fourth, log stimulus—response discriminability values between physically adjacent conditional stimuli summed to values that were not significantly different from estimates of the discriminability values for conditional stimuli that were spaced further apart.     

Common spatial organization of number and emotional expression: a mental magnitude line

Converging behavioral and neural evidence suggests that numerical representations are mentally organized in left-to-right orientation. Here we show that this format of spatial organization extends to emotional expression. In Experiment 1, right-side responses became increasingly faster as number (represented by Arabic numerals) or happiness (depicted in facial stimuli) increased, for judgments completely unrelated to magnitude. Additional experiments suggest that magnitude (i.e., more/less relations), not valence (i.e., positive/negative), underlies left-to-right orientation of emotional expression (Experiment 2), and that this orientation accommodates to the context-relevant emotion (e.g., happier faces are more rightward when judged on happiness, but more leftward when judged on angriness; Experiment 3). These findings show that people automatically extract magnitude from a variety of stimuli, representing such information in common left-to-right format, perhaps reflecting a mental magnitude line. We suggest that number is but one dimension in a hyper-general representational system uniting disparate dimensions of magnitude and likely subserved by common neural mechanisms in posterior parietal cortex.     

Local and Global Sources of Control in Pigeon Delayed Matching-to-sample Performance

The present study employed a behavioural detection approach to investigate the combined effects of sample duration and sample presentation frequency on delayed matching accuracy of pigeons. Experiment 1 showed that when both samples were exposed at each of the two possible durations within a two-alternative, delayed matching session, discriminability was higher to the longer duration sample than to the short-duration sample, as found when sample duration is varied between sessions. Experiment 2's asymmetrical procedure increased bias toward the more frequent of the two samples but had no influence on discriminability. Initial discriminability was higher to samples exposed for longer durations, irrespective of stimulus presentation frequency. The results suggest qualitatively different effects of the two sources of stimulus control under consideration: Sample duration (a local or within-trial manipulation) exerted its effect on discrimination of the stimuli, whereas sample presentation frequence (a global factor) exerted its major effect on response bias. An interpretation of the data in terms of Blough's (1996) analysis of errors in matching tasks suggests that the amount of behaviour under control of the sample stimulus markedly changed with different sample durations. The analysis also showed that the biasing manipulation exerted most of its effect on the portion of behaviour outside of control by the critical stimulus. We argue that theoretical accounts of delayed matching performance need to consider both local and global factors as determinants of matching accuracy.     

Are Arabic and verbal numbers processed in different ways?

Four experiments were conducted in order to examine effects of notation--Arabic and verbal numbers--on relevant and irrelevant numerical processing. In Experiment 1, notation interacted with the numerical distance effect, and irrelevant physical size affected numerical processing (i.e., size congruity effect) for both notations but to a lesser degree for verbal numbers. In contrast, size congruity had no effect when verbal numbers were the irrelevant dimension. In Experiments 2 and 3, different parameters that could possibly affect the results, such as discriminability and variability (Experiment 2) and the block design (Experiment 3), were controlled. The results replicated the effects obtained in Experiment 1. In Experiment 4, in which physical size was made more difficult to process, size congruity for irrelevant verbal numbers was observed. The present results imply that notation affects numerical processing and that Arabic and verbal numbers are represented separately, and thus it is suggested that current models of numerical processing should have separate comparison mechanisms for verbal and Arabic numbers.     

刺激的知觉辨认难度与大脑两半球间的分布式加工

采用半视野速示术将标准刺激在中间视野呈现,比较刺激以不同偏心视角（3.5°,5°和6.5°）在左或右视野同时呈现,以检查不同偏心视角引起比较刺激知觉辨认难度的改变对汉字大写数字奇－偶概念同/异判断任务在大脑两半球间分布式加工的影响。结果显示：随偏心视角的增大正确反应时和错误百分数均显著提高;三种视角条件下左右手的正确反应时均有明显的右视野（左半球）优势;3.5°视角右视野（左半球）呈现时右手反应明显快于左手,5°视角右视野（左半球）与左视野（右半球）呈现时均为右手反应明显快于左手,6.5°视角右视野（左半球）与左视野（右半球）呈现时均为左手反应明显快于右手。这些结果提示：本研究条件下只有比较刺激在6.5°偏心视角呈现时刺激和反应可能出现大脑两半球间分布式加工,3.5°和5°视角呈现时可能为左半球单独加工。6.5°视角刺激呈现的分布加工明显由于大视角呈现时比较刺激辨认难度与注意要求的提高所致。     

A partial repetition effect in choice reaction time for multidimensional stimuli

Bertelson (1963), and others more recently, have observed that when the same stimulus is presented consecutively the reaction time (RT) to the second presentation is faster than the RT to the first presentation. In Experiments 1 and 2, two-dimensional stimuli are used in a discrete four-choice RT task where the stimuli can either be completely repeated, partially repeated, or completely different. In Experiment 3, three-dimensional stimuli were used in a discrete eight-choice RT task where the stimuli can either be completely repeated, partially respeated with respect to two dimensions, partially repeated with respect to one dimension, or completely different. The partial repetition of multidimensional stimuli showed a significant facilitation effect on RT with all sets of stimuli used in the present experiments. This result is discussed in respect to the various possible loci of the repetition effect.     

Ordinality and inferential abilities of a grey parrot (Psittacus erithacus)

A grey parrot (Psittacus erithacus), able to label the color of the bigger or smaller object in a pair (I. M. Pepperberg & M. V. Brezinsky, 1991), to vocally quantify < or =6 item sets (including heterogeneous subsets; I. M. Pepperberg, 1994), and separately trained to identify Arabic numerals 1-6 with the same vocal English labels but not to associate Arabic numbers with their relevant physical quantities, was shown pairs of Arabic numbers or an Arabic numeral and a set of objects and was asked for the color of the bigger or smaller one. The parrot's success showed he (a) understood number symbols as abstract representations of real-world collections, (b) inferred the relationship between the Arabic number and the quantity via stimulus equivalence, and (c) understood the ordinal relationship of his numbers.     

Detecting conjunctions of color and form in parallel

Researchers have proposed that graphical efficacy may be determined, in part, by the nature of the perceptual interactions that exist between attributes used to create graphical displays. One extreme type of interaction isintegrality, in which two or more physical dimensions are represented as a single psychological dimension in the observer. An alternative type of interaction isconfigurality, in which a global emergent dimension is availableto the observer in addition to the component attributes. Thirteen stimulus sets, each composed of attributes commonly used in the design of graphs, were submitted to the performance-based diagnostics of integrality and configurality. Analyses suggest a continuum of configurality among the present stimulus sets, with little evidence for integral graphical attributes. The configural pattern of results was more common when two identical dimensions were paired (homogeneous stimuli) than when two different dimensions were paired (heterogeneous stimuli). However, there was no evidence that pairs of dimensions belonging to a single object (object integration) were any more configural than dimensions belonging to different objects. Object integration was, however, consistently related to inefficient performance in tasks requiring the filtering of one of two component dimensions.     

Dimensional dominance and stimulus discriminability.

The relationship between the discriminability of scaling stimuli and assessed dimensional dominance was investigated in three studies. Sixty kindergarten children were assessed using a psychophysical scaling method to determine JND values for the size, brightness, and orientation dimensions. Thirty of the same subjects were then assessed for dimensional dominance using stimuli of two levels of known discriminability, based on the obtained JND values. In a third experiment, the remaining 30 subjects were assessed for dimensional dominance using stimuli that systematically emphasized the values of one dimension relative to the other two dimensions, again based on obtained JND values.The results indicated that (1) kindergarten children were able to perform consistently during psychophysical scaling, and there was little variability between children in their judgments of stimuli, (2) the overall level of discriminability affects dimensional dominance scaling behavior, with subjects more likely to exhibit dominance for one dimension when all the values of scaling stimuli are high in discriminability, and (3) some support for the hypothesis that dimensional dominance scaling behavior can be manipulated by manipulating the relative discriminability of scaling stimuli was found, though the trend was not clear.The relative discriminability of scaling stimuli appears to have some effects on dimensional dominance scaling behavior of young children. However, some pre-experimental bias to attend to a particular dimension seems to remain even when the values of all dimensions present are of equal and known discriminability. Dimensional dominance is a function of an interaction between discriminability of scaling stimuli and the experiential bias or perceptual set of the subject.     

ELECTROPHYSIOLOGICAL CORRELATES OF STIMULUS EQUIVALENCE PROCESSES

Research reported here concerns neural processes relating to stimulus equivalence class formation. In Experiment 1, two types of word pairs were presented successively to normally capable adults. In one type, the words had related usage in English (e.g., uncle, aunt). In the other, the two words were not typically related in their usage (e.g., wrist, corn). For pairs of both types, event‐related cortical potentials were recorded during and immediately after the presentation of the second word. The obtained waveforms differentiated these two types of pairs. For the unrelated pairs, the waveforms were significantly more negative about 400 ms after the second word was presented, thus replicating the “N400” phenomenon of the cognitive neuroscience literature. In addition, there was a strong positive‐tending wave form difference post‐stimulus presentation (peaked at about 500 ms) that also differentiated the unrelated from related stimulus pairs. In Experiment 2, the procedures were extended to study arbitrary stimulus—stimulus relations established via matching‐to‐sample training. Participants were experimentally näive adults. Sample stimuli (Set A) were trigrams, and comparison stimuli (Sets B, C, D, E, and F) were nonrepresentative forms. Behavioral tests evaluated potentially emergent equivalence relations (i.e., BD, DF, CE, etc.). All participants exhibited classes consistent with the arbitrary matching training. They were also exposed also to an event‐related potential procedure like that used in Experiment 1. Some received the ERP procedure before equivalence tests and some after. Only those participants who received ERP procedures after equivalence tests exhibited robust N400 differentiation initially. The positivity observed in Experiment 1 was absent for all participants. These results support speculations that equivalence tests may provide contextual support for the formation of equivalence classes including those that emerge gradually during testing.     

Ordinal judgments of symbolic stimuli by capuchin monkeys (Cebus apella) and rhesus monkeys (Macaca mulatta): the effects of differential and nondifferential reward

Ordinal learning was investigated in capuchin monkeys (Cebus apella) and rhesus monkeys (Macaca mulatta). In Experiment 1, both species were presented with pairings of the Arabic numerals 0 to 9. Some monkeys were given food rewards equal to the value of the numeral selected and some were rewarded with a single pellet only for choosing the higher numeral within the pair. Both species learned to select the larger numeral, but only rhesus monkeys that were differentially rewarded performed above chance levels when presented with novel probe pairings. In Experiment 2, the monkeys were first presented with arrays of 5 familiar numerals (from the range 0 to 9) and then arrays of 5 novel letters (from the range A to J) with the same reward outcomes in place as in Experiment 1. Both species performed better with the numerals, suggesting that an ordinal sequence of all stimuli had been learned during Experiment 1, rather than a matrix of two-choice discriminations.     

Use of number by crows: investigation by matching and oddity learning

Hooded crows were trained in two-alternative simultaneous matching and oddity tasks with stimulus sets of three different categories: color (black and white), shape (Arabic Numerals 1 and 2, which were used as visual shapes only), and number of elements (arrays of one and two items). These three sets were used for training successively and repeatedly; the stimulus set was changed to the next one after the criterion (80% correct or better over 30 consecutive trials) was reached with the previous one. Training was continued until the criterion could be reached within the first 30 to 50 trials for each of the three training sets. During partial transfer tests, familiar stimuli (numerals and arrays in the range from 1 to 2) were paired with novel ones (numerals and arrays in the range from 3 to 4). At the final stage of testing only novel stimuli were presented (numerals and arrays in the range from 5 to 8). Four of 6 birds were able to transfer in these tests, and their performance was significantly above chance. Moreover, performance of the birds on the array stimuli did not differ from their performance on the color or shape stimuli. They were capable of recognizing the number of elements in arrays and comparing the stimuli by this attribute. It was concluded that crows were able to apply the matching (or oddity) concept to stimuli of numerical category.     

Influence of auditory and audiovisual stimuli on the right–left prevalence effect

When auditory stimuli are used in two-dimensional spatial compatibility tasks, where the stimulus and response configurations vary along the horizontal and vertical dimensions simultaneously, a right–left prevalence effect occurs in which horizontal compatibility dominates over vertical compatibility. The right–left prevalence effects obtained with auditory stimuli are typically larger than that obtained with visual stimuli even though less attention should be demanded from the horizontal dimension in auditory processing. In the present study, we examined whether auditory or visual dominance occurs when the two-dimensional stimuli are audiovisual, as well as whether there will be cross-modal facilitation of response selection for the horizontal and vertical dimensions. We also examined whether there is an additional benefit of adding a pitch dimension to the auditory stimulus to facilitate vertical coding through use of the spatial-musical association of response codes (SMARC) effect, where pitch is coded in terms of height in space. In Experiment 1, we found a larger right–left prevalence effect for unimodal auditory than visual stimuli. Neutral, non-pitch coded, audiovisual stimuli did not result in cross-modal facilitation, but did show evidence of visual dominance. The right–left prevalence effect was eliminated in the presence of SMARC audiovisual stimuli, but the effect influenced horizontal rather than vertical coding. Experiment 2 showed that the influence of the pitch dimension was not in terms of influencing response selection on a trial-to-trial basis, but in terms of altering the salience of the task environment. Taken together, these findings indicate that in the absence of salient vertical cues, auditory and audiovisual stimuli tend to be coded along the horizontal dimension and vision tends to dominate audition in this two-dimensional spatial stimulus–response task.