The mental representation of numerical fractions: real or integer?

Numerical fractions are commonly used to express ratios and proportions (i.e., real numbers), but little is known about how they are mentally represented and processed by skilled adults. Four experiments employed comparison tasks to investigate the distance effect and the effect of the spatial numerical association of response codes (SNARC) for fractions. Results showed that fractions were processed componentially and that the real numerical value of the fraction was not accessed, indicating that processing the fraction's magnitude is not automatic. In contrast, responses were influenced by the numerical magnitude of the components and reflected the simple comparison between numerators, denominators, and reference, depending on the strategy adopted. Strategies were used even by highly skilled participants and were flexibly adapted to the specific experimental context. In line with results on the whole number bias in children, these findings suggest that the understanding of fractions is rooted in the ability to represent discrete numerosities (i.e., integers) rather than real numbers and that the well-known difficulties of children in mastering fractions are circumvented by skilled adults through a flexible use of strategies based on the integer components.     

Exercise commitment and proneness to eating disorders in a group of physical education teachers

The study examined the association of exercise commitment with proneness to eating disorders in 50 physical education teachers who had been practicing various aerobic sports at least three times a week for at least 5 years. Significant coefficients were found between Commitment to Exercise Scale scores, the number of weekly training sessions, and scores on the Eating Disorders Inventory-2 scales measuring Maturity Fears, Social Insecurity, Perfectionism, and Asceticism. However, no relationship was found between the Commitment to Exercise Scale and the Eating Disorders Inventory-2 variables measuring anorexic tendencies (such as Drive for Thinness, Body Dissatisfaction, and Bulimia). Findings suggest the presence of some psychological factors common to both anorexic tendencies and excessive exercising but not complete overlap, so a rather more complex pattern of relationships appears to be mediated by sex and personality characteristics.     

A Probability Measure for Partial Events

We introduce the concept of partial event as a pair of disjoint sets, respectively the favorable and the unfavorable cases. Partial events can be seen as a De Morgan algebra with a single fixed point for the complement. We introduce the concept of a measure of partial probability, based on a set of axioms resembling Kolmogoroff’s. Finally we define a concept of conditional probability for partial events and apply this concept to the analysis of the two-slit experiment in quantum mechanics.     

Comparison processes on visual mental images

Three experiments were conducted to test whether visual mental images and visual perceptual representations possess equivalent structural properties and undergo functionally equivalent comparison processes. In Experiment 1, subjects were required to perform asame-different letter classification in which the two letters were shown in succession. The first letter in the pair either was actually presented (perceptual condition) or had to be actively generated (imaginal condition). Both conditions showed that (1) response latencies fordifferent decisions decreased as a function of the degree of difference (segment effect), and (2) same decisions were faster than the fastestdifferent ones (fast same effect). In Experiment 2, the imaginal condition only was employed, but no imagery instructions were given and very strict time constraints were assigned. In spite of these restrictions, subjects apparently generated and used visual images, as attested by the fact that the results were comparable to those of the previous experiment. In Experiment 3, three experimental manipulations were introduced to prevent the use of visual images. Such manipulations proved effective, as shown by the disappearance of the segment effect. It was concluded that in the visual modality images and percepts are equivalent in structure and are processed in a very similar way.     

Can linguistics contribute to the study of verbal behavior?

A number of publications during the last decade reveal a growing interest in linguistics and psycholinguistics among some radical behaviorists, who have proposed a direct rapprochement between a formal analysis of language and a functional account. It is argued that whereas function has to do with the circumstances under which verbal behavior is emitted, structure has to do with its "internal organization," the ways in which sentences or parts thereof are presumably interrelated. These are said to be different dimensions of verbal behavior; together they should lead toward a coherent psychology of language. But psychologists bent on incorporating techniques from linguistics should be aware of its underlying assumptions, lest their work be deflected in essentially unproductive directions. The line between rapprochement and subservience is thin indeed, as the extant literature shows. This paper traces the development of mainstream contemporary psycholinguistics and examines the linguist's assumptions about the subject matter in the light of a behavioral analysis. The possibility of an effective reconciliation seems to be a long way off.     

Lesion-symptom mapping of language impairments in people with brain tumours: The influence of linguistic stimuli

People with tumours in specific brain sites might face difficulties in tasks with different linguistic material. Previous lesion-symptom mapping studies (VLSM) demonstrated that people with tumours in posterior temporal regions have more severe linguistic impairments. However, to the best of our knowledge, preoperative performance and lesion location on tasks with different linguistic stimuli have not been examined. In the present study, we performed VLSM on 52 people with left gliomas to examine whether tumour distribution differs depending on the tasks of the Aachen Aphasia Test. The VLSM analysis revealed that single-word production (e.g. object naming) was associated with the inferior parietal lobe and that compound and sentence production were additionally associated with posterior temporal gyri. Word repetition was affected in people with tumours in inferior parietal areas, whereas sentence repetition was the only task to be associated with frontal regions. Subcortically, word and sentence production were found to be affected in people with tumours reaching the arcuate fasciculus, and compound production was primarily associated with tumours affecting the inferior longitudinal and inferior fronto-occipital fasciculus. Our work shows that tasks with linguistic stimuli other than single-word naming (e.g. compound and sentence production) relate to additional cortical and subcortical brain areas. At a clinical level, we show that tasks that target the same processes (e.g. repetition) can have different neural correlates depending on the linguistic stimuli used. Also, we highlight the importance of left temporoparietal areas.     

Proof Analysis in Modal Logic

A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics is presented. The method covers all modal logics characterized by Kripke frames determined by universal or geometric properties and it can be extended to treat also Gödel–Löb provability logic. The calculi provide direct decision methods through terminating proof search. Syntactic proofs of modal undefinability results are obtained in the form of conservativity theorems.     

Visuospatial priming of the mental number line

It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response selection. A spatial prime is processed faster than a numerical target, and consistent with our hypothesis, we found that such a spatial prime affects non-spatial, verbal responses more when the prime follows a numerical target (backward priming) then when it precedes it (forward priming). This finding emerged both in a number-comparison and a parity judgment task, and cannot be ascribed to a "Spatial-Numerical Association of Response Codes" (SNARC). Contrary to some earlier claims, we therefore conclude that visuospatial-numerical interactions do occur, even before response selection.     

Temporal order judgment reveals how number magnitude affects visuospatial attention

The existence of spatial components in the mental representation of number magnitude has raised the question regarding the relation between numbers and spatial attention. We present six experiments in which this relation was examined using a temporal order judgment task to index attentional allocation. Results demonstrate that one important consequence of numerical processing is the automatic allocation of spatial attention, which in turn affects the perception of the temporal order of visual events. Given equal onset time, left-side stimuli are perceived to occur before right-side stimuli when a small number (1, 2) is processed, whereas right-side stimuli are perceived to occur before left-side stimuli when a larger number (8, 9) is processed. In addition, we show that this attentional effect is specific to quantity processing and does not generalize to non-numerical ordinal sequences.     

Right-left prevalence effect with horizontal and vertical effectors

We investigated the right-left prevalence effect in spatial compatibility tasks by assessing subjects' performance on a two-dimensional task in which both the horizontal and vertical spatial dimensions were task relevant. Two experiments were performed, in which stimulus-response mappings were one-dimensional (Experiment 1) and two-dimensional (Experiment 2). The subjects responded by using either horizontal or vertical effectors to stimuli appearing in four possible locations. With the one-dimensional mapping, the spatial compatibility effect was present only in the dimension relevant to the mapping. With the two-dimensional mapping, the horizontal compatibility effect was always present, whereas the vertical compatibility effect was present only when vertical effectors were used. This pattern of results indicates that horizontal coding takes place with either horizontal or vertical effectors, whereas vertical coding takes place only when vertical effectors are used.