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     

Positive and Negative Hypothesis Testing by Cooperative Groups

In a rule induction problem positive hypothesis tests select evidence that the tester expects to be an example of the correct rule if the hypothesis is correct, whereas negative hypothesis tests select evidence that the tester expects to be a nonexample if the hypothesis is correct. Previous research indicates the general effectiveness of a positive test strategy for individuals, but there has been very little research with cooperative groups. We extend the analysis of Klayman and Ha (Psychological Review, 1987) of ambiguous verification or conclusive falsification of five possible types of hypotheses by positive and negative tests by emphasizing the importance of further examples following hypothesis tests. In two experiments four-person cooperative groups solved rule induction problems by proposing a hypothesis and selecting evidence to test the hypothesis on each of four arrays on each trial. In different conditions the groups were instructed to use different combinations of positive and negative tests on the four arrays. Positive tests were more likely to lead to further examples than negative tests, and the proportion of correct hypotheses corresponded to the proportion of positive tests, in both experiments. We suggest that positive tests are more effective than negative hypothesis tests in generating further evidence, and thus in inducing the correct rule, in experimental rule induction tasks with a criterion of certainty imposed by the researcher.     

SEEING TWO AS ONE:

Abstract -Object tokens are episodic visual representations that mediate the ability to track visual events as they move about and change over time. Multiple tokens also allow the viewer to individuate multiple instances of a single type of object. In the present study, we established a functional link for object tokens in two seemingly disparate visual phenomena: apparent motion and repetition blindness [RB]. In RB, repeated items are more difficult to perceive than unre-peated items. Using displays in which two sets of alphanumeric characters streamed in opposite directions across a computer screen in apparent motion, we found increased RB for targets appearing within a single apparent motion stream, relative to targets in different apparent motion streams. The results are inconsistent with refractory period or memory retrieval accounts of RB and support the role of object tokens in both apparent motion and RB.     

Referenzsemantik in der Partnermodellierung

How can we explain that an assertion on something perceived can be understood in the same manner by somebody who cannot perceive that scene? This problem bases the interest in computational linguistics in how listener modeling could possibly be harmonized with reference semantics. Mental images substituting real perception appear as a way out. The architecture of the listener model has to be adapted to the creation and use of such pictorial data structures. Furthermore, the relation between the latter and a verbal (i. e., propositional) representation must be understood. The resulting architecture of a listener model with reference semantics can be employed to solve communicational problems from three general classes in a better way, as is demonstrated by an example implementation.     

Simulation and the Reproduction of Injustice: A Reply

Melinda Vadas rejects my claim that there are morally relevant differences between simulations of unjust events and actual unjust events on the ground that I overlook the connection between simulations and that which they simulate. I argue that this purported moral connection can only be understood as either the result of a necessary psychological disposition or as a “magical,” metaphysical attachment, neither of which is defensible or satisfactory.     

The holocaust of first nation people: Residual effects on parenting and treatment implications

The residential school experience was devastating for many First Nation (Indian) people. The lingering effects of this era have been far reaching and remain painfully evident throughout Native communities. One of the more obvious areas directly affected has been parenting. This paper discusses current parenting difficulties of Native clients who were formerly in residential schools. A connection is made between the abuse experienced by these individuals and their parental struggles. Along with addressing various sociopolitical issues, a number of clinical interventions designed to promote the healing process of these victims and their families are provided and discussed.     

Predictors of Developmental Task Attainment for Young Adults from Divorced Families

To determine which variables impact developmental task attainment for young adults from divorced families, respondents completed demographic questions, the young adult version of the Personal Authority in the Family System Questionnaire, and the three family relationship subscales of the Family Environment Scale. Of the factors assessed, results suggest that the quality of post-divorce family functioning is the most salient predictor of development for young adults from divorced families. Additionally, although conflict and cohesion have unique effects on task attainment for young adults, expressiveness appears to be the dimension of post divorce family functioning most related to young adult development.