The visuospatial functions in children after cerebellar low‐grade astrocytoma surgery: A contribution to the pediatric neuropsychology of the cerebellum

The aim of this study was to specify whether cerebellar lesions cause visuospatial impairments in children. The study sample consisted of 40 children with low‐grade cerebellar astrocytoma, who underwent surgical treatment and 40 healthy controls matched with regard to age and sex. Visuospatial abilities were tested using the spatial WISC‐R subtests (Block Design and Object Assembly), Rey–Osterrieth Complex Figure, Benton Judgment of Line Orientation Test, PEBL Mental Rotation Task, and Benton Visual Retention Test. To exclude general diffuse intellectual dysfunction, the WISC‐R Verbal Intelligence IQ, Performance IQ, and Full‐Scale IQ scores were analysed. Post‐surgical medical consequences were measured with the International Cooperative Ataxia Rating Scale. Compared to controls, the cerebellar group manifested problems with mental rotation of objects, visuospatial organization, planning, and spatial construction processes which could not be explained by medical complications or general intellectual retardation. The intensity of visuospatial syndrome highly depends on cerebellar lesion side. Patients with left‐sided cerebellar lesions display more severe spatial problems than those with right‐sided cerebellar lesions. In conclusion, focal cerebellar lesions in children affect their visuospatial ability. The impairments profile is characterized by deficits in complex spatial processes such as visuospatial organization and mental rotation, requiring reconstruction of visual stimuli using the imagination, while elementary sensory analysis and perception as well as spatial processes requiring direct manipulation of objects are relatively better preserved. This pattern is analogous to the one previously observed in adult population and appears to be typical for cerebellar pathology in general, regardless of age.     

Logical rules of visual brain: From anatomy through neurophysiology to cognition

Humans can easily recognize objects as complex as faces even if they have not seen them in such conditions or context before. It seems that perceptually we are insensitive to the exact properties of an object’s parts but the same parts in different configurations or contexts may introduce contradictory effects. From a computational point of view, we are often insensitive to changes of some symbols, but the same symbols may lead to different classification of the same object. In present work we are looking for the anatomical and neurophysiological basis of these perceptual effects. We describe interactions between parts and their configurations in different areas of the visual brain on the basis of a single cell electrophysiological activity in the thalamus, and cortical areas V1 and V4. Our model is based on feedforward (FF) and feedback (FB) interactions between these areas. In the retina and thalamus simple light spots are classified, V1 is the first area extracting edge orientation and V4 is the first area sensitive to simple shapes. The FF pathways combine properties extracted in each area into hypothetical objects. Area V1 presents concepts of orientations, while area V4 presents concepts of a simple shape. The FB pathways are responsible for comparison of the learned concepts with extracted object’s properties – they form predictions. In each area structure related predictions are tested against hypothesis. We formulate a theory in which different visual stimuli are described through their condition attributes: responses in LGN, V1, and V4 neurons are divided into several ranges and are treated as decision attributes. Applying rough set theory [Pawlak, Z. (1991). Rough sets – theoretical aspects of reasoning about data. Boston, London, Dordrecht: Kluwer Academic Publishers] we have divided our stimuli into area dependent equivalent classes. We propose that relationships between decision rules in each area are determined by two different logical rules: “driver logical rule” of FF and “modulator logical rule” of FB pathways. These interactions are proposed to be a neurophysiological basis of the object classification.     

Socratic Proofs for Quantifiers

First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given. *Research for this paper was supported by The Foundation for Polish Science (both authors), and indirectly (in the case of the first author) by a bilateral exchange project funded by the Ministry of the Flemish Community (project BIL 01/80) and the State Committee for Scientific Research, Poland.     

A conjunction in closure spaces

This paper is closely related to investigations of abstract properties of basic logical notions expressible in terms of closure spaces as they were begun by A. Tarski (see [6]). We shall prove many properties of ω-conjunctive closure spaces (X is ω-conjunctive provided that for every two elements of X their conjunction in X exists). For example we prove the following theorems:

1. For every closed and proper subset of an ω-conjunctive closure space its interior is empty (i.e. it is a boundary set).
2. If X is an ω-conjunctive closure space which satisfies the ω-compactness theorem and \(\hat P\) [X] is a meet-distributive semilattice (see [3]), then the lattice of all closed subsets in X is a Heyting lattice.
3. A closure space is linear iff it is an ω-conjunctive and topological space.
4. Every continuous function preserves all conjunctions.

     

Erotetic arguments: A preliminary analysis

The concept of erotetic argument is introduced. Two relations between sets of declarative sentences and questions are analysed; and two classes of erotetic arguments are characterized.     

Significant subtest score differences on the WISC-R

Psychologists must often make decisions about the significance of scaled score differences between subtests on the WISC-R. Differences which statistically significant at the .05 and .01 level are presented. Generally, minimum differences of 3 to 5 points are necessary at the .05 level and 4 to 6 points at the .01 level. Cautions concerning the interpretation of statistically significant differences are discussed.