Fractal Images of Formal Systems

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex value spaces, with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic.\looseness=-1     

Local and global factors of similarity in visual search

Effects of the similarity between target and distractors in a visual search task were investigated in several experiments. Both familiar (numerals and letters) and unfamiliar (connected figures in a 5 × 5 matrix) stimuli were used. The observer had to report on the presence or absence of a target among a variable number of homogeneous distractors as fast and as accurately as possible. It was found that physical difference had the same clear effect on processing time far familiar and for unfamiliar stimuli: processing time decreased monotonically with increasing physical difference. Distractors unrelated to the target and those related to the target by a simple transformation (180° rotation, horizontal or vertical reflection) were also compared, while the physical difference was kept constant. For familiar stimuli, transformational relatedness increased processing time in comparison with that fort unrelated stimulus pairs. It was further shown in a scaling experiment that this effect could be accounted for by the amount of perceived similarity of the target-distractor pairs. For unfamiliar stimuli, transformational relatedness did have a smaller and less pronounced effect. Various comparable unrelated distractors resulted in a full range of processing times. Results from a similarity scaling experiment correlated well with the outcome of the experiments with unfamiliar stimuli. These results are interpreted in terms of an underlying continuum of perceived similarity as the basis of the speed of visual search, rather than a dichotomy of parallel versus serial processing.     

The effect of social support on prenatal care.

This article examines the effects of social support on the receipt of adequate prenatal care. A study was conducted to test the hypotheses that social support helps women overcome obstacles to obtaining such care, and that social support has greater effects on women facing the most obstacles. Survey data were gathered for more than 90% of the women who gave birth in Oklahoma hospitals during specific periods in the summer of 1986. The authors found only weak support for the first hypothesis, and for the second hypothesis found only support that must be qualified according to the measure of social support. Strong evidence indicates, however, that difficulty in paying for prenatal care, personal inconveniences, and unwanted pregnancies are obstacles to obtaining such care. The findings account for some of the frequently observed demographic differences associated with receipt of adequate prenatal care, although such differences persisted even after the obstacles were considered. The authors present implications for policy makers seeking to improve women's receipt of adequate prenatal care.     

A model for the study of research and education in a transdisciplinary context

In an evaluation project at the Goteborg University, we have looked at the relationship between individual and collective production of knowledge within the Health sciences in order to facilitate a common ground for a Academy of Health Sciences. We found obstacles for developing an environment which could stimulate multilateral co-operation and creativity. Some of these obstacles have their root in the different cultural backgrounds indicated in the analysis and makes it difficult to find common aims and strategies. The Model used makes the organizations’ activities visible and encouraging transdisciplinary contacts and improve organizational, structural and ideological decision making emanating from overall policies of the boards concerned.     

Pharmacological dissociation of memory: anisomycin, a protein synthesis inhibitor, and leupeptin, a protease inhibitor, block different learning tasks

Inhibition of protein synthesis by anisomycin for a short duration impairs memory of a one-trial inhibitory avoidance task in rats. Memory of escape conditioning involving eight trials is disrupted only if the duration of protein synthesis is prolonged by repeated injections. In marked contrast, olfactory memory of rats trained on two odor discriminations is not affected by anisomycin even if the duration of inhibition is prolonged and the number of trials is reduced to a minimum. In previous work, leupeptin, a thiol proteinase inhibitor, was shown to impair olfactory discrimination learning, but left inhibitory and avoidance conditioning intact. Together, these results provide a pharmacological double dissociation of memory, and suggest that the same chemistries, or mixtures of chemistries, may not be involved in all types of memory.     

Differential indications for desipramine--results of a controlled multiclinical study]

The antidepressants desipramine and imipramine were compared within the framework of a multiclinical study performed under the conditions of a controlled clinical experiment. There has been found a time-different remission of affective symptoms, which was not detectable for the inhibition of drive. The tachythymoleptic action of desipramine is discussed with reference to these results. Evaluation of the possibility of controlling affects shows different ranges of activity of desipramine and imipramine, with desipramine influencing especially negative psychoenergetic symptoms in the area of drives and emotions and imipramine, restrictive symptoms in addition to differential phenomena of the psychomotor expression.     

The effect of punishment and reinforcement procedures on a stutterer's factor II avoidance response

The purpose of this clinical experiment was to investigate the manipulability of a Factor II avoidance response (arm movement). The substantive hypothesis under test was that its suppression would be enhanced by repeated punishment sessions. During the first of nine therapy sessions response-contingent negative stimulation was not delivered. In the next five, after a base-rate period, “wrong” was made consequent upon the target response. In each of these sessions the suppression of arm movement was apparent. However, the magnitude of the suppression decreased from session to session. Evidently, the continued use of punishment did not enhance suppression. Because of this finding procedural changes were introduced in the next three therapy sessions. Verbal praise was added as a consequence of increasingly stringent omission criteria and three consecutive units of praise led to time-out from the reportedly fatiguing task of continuous speech. A marked reduction and then complete extinction resulted. Moreover, learning was evidenced since the frequency of arm movement lessened in the base-rate period of each session.     

Effects of Viewing “Holocaust” on Germans and Americans: A Just-World Analysis1

This study examines attributions of blame to the Nazis and the Jews for the events of the holocaust. The sample consisted of Germans and Americans who had viewed the television series “Holocaust” and comparison groups who had not seen the program. It was found that among viewers who identified with the Nazis, attributions of blame to the Jews were higher than among nonviewers or viewers who identified with the Jews. Attributions of blame to the Nazis did not vary as a function of viewing the television series. However, people who identified with the Nazis blamed the Nazis less for the holocaust than people who identified with the Jews. These results are discussed in terms of the justworld hypothesis (Lerner & Miller, 1978) and their implications for media presentations on the victims of oppression.     

On the conflict between logic and belief in syllogistic reasoning

Three experiments are reported that investigate the weighting attached to logic and belief in syllogistic reasoning. Substantial belief biases were observed despite controls for possible conversions of the premises. Equally substantial effects of logic were observed despite controls for two possible response biases. A consistent interaction between belief and logic was also recorded; belief bias was more marked on invalid than on valid syllogisms. In all experiments, verbal protocols were recorded and analyzed. These protocols are interpreted in some cases as providing rationalizations for prejudiced decisions and, in other cases, as reflecting a genuine process of premise to conclusion reasoning. In the latter cases, belief bias was minimal but still present. Similarly, even subjects who focus primarily on the conclusion are influenced to an extent by the logic. Thus a conflict between logic and belief is observed throughout, but at several levels of extent.