Arithmetic based on the Church numerals in illative combinatory logic

In the early thirties, Church developed predicate calculus within a system based on lambda calculus. Rosser and Kleene developed Arithmetic within this system, but using a Godelization technique showed the system to be inconsistent.Alternative systems to that of Church have been developed, but so far more complex definitions of the natural numbers have had to be used. The present paper based on a system of illative combinatory logic developed previously by the author, does allow the use of the Church numerals. Given a new definition of equality all the Peano-type axioms of Mendelson except one can be derived. A rather weak extra axiom allows the proof of the remaining Peano axiom. Note. The illative combinatory logic used in this paper is similar to the logic employed in computer languages such as ML.The author wishes to thank Dr. Roger Hindley for proofreading this paper and for making some useful suggestions. This paper was presented at the 1986 Annual Conference of the Australasian Association of Logic in Auckland, 9–12 July, 1986.     

A representation theorem for languages with generalized quantifiers through back-and-forth methods

We obtain in this paper a representation of the formulae of extensions ofL by generalized quantifiers through functors between categories of first-order structures and partial isomorphisms. The main tool in the proofs is the back-and-forth technique. As a corollary we obtain the Caicedo's version of Fraïssés theorem characterizing elementary equivalence for such languages. We also discuss informally some geometrical interpretations of our results.     

Perception of translational heading from optical flow

Radial patterns of optical flow produced by observer translation could be used to perceive the direction of self-movement during locomotion, and a number of formal analyses of such patterns have recently appeared. However, there is comparatively little empirical research on the perception of heading from optical flow, and what data there are indicate surprisingly poor performance, with heading errors on the order of 5 degrees-10 degrees. We examined heading judgments during translation parallel, perpendicular, and at oblique angles to a random-dot plane, varying observer speed and dot density. Using a discrimination task, we found that heading accuracy improved by an order of magnitude, with 75%-correct thresholds of 0.66 degrees in the highest speed and density condition and 1.2 degrees generally. Performance remained high with displays of 63-10 dots, but it dropped significantly with only 2 dots; there was no consistent speed effect and no effect of angle of approach to the surface. The results are inconsistent with theories based on the local focus of outflow, local motion parallax, multiple fixations, differential motion parallax, and the local maximum of divergence. But they are consistent with Gibson's (1950) original global radial outflow hypothesis for perception of heading during translation.     

Problem structure and the use of base-rate information from experience

This article is concerned with the use of base-rate information that is derived from experience in classifying examples of a category. The basic task involved simulated medical decision making in which participants learned to diagnose hypothetical diseases on the basis of symptom information. Alternative diseases differed in their relative frequency or base rates of occurrence. In five experiments initial learning was followed by a series of transfer tests designed to index the use of base-rate information. On these tests, patterns of symptoms were presented that suggested more than one disease and were therefore ambiguous. The alternative or candidate diseases on such tests could differ in their relative frequency of occurrence during learning. For example, a symptom might be presented that had appeared with both a relatively common and a relatively rare disease. If participants are using base-rate information appropriately (according to Bayes' theorem), then they should be more likely to predict that the common disease is present than that the rare disease is present on such ambiguous tests. Current classification models differ in their predictions concerning the use of base-rate information. For example, most prototype models imply an insensitivity to base-rate information, whereas many exemplar-based classification models predict appropriate use of base-rate information. The results reveal a consistent but complex pattern. Depending on the category structure and the nature of the ambiguous tests, participants use base-rate information appropriately, ignore base-rate information, or use base-rate information inappropriately (predict that the rare disease is more likely to be present). To our knowledge, no current categorization model predicts this pattern of results. To account for these results, a new model is described incorporating the ideas of property or symptom competition and context-sensitive retrieval.     

Understanding the central processing limit in consistent-mapping visual search tasks

Effects of load (i.e., the number of stimuli in the display) have been observed in multiple-frame studies using a consistent mapping of stimuli to responses (e.g., Fisher, 1982, 1984). In a series of four experiments, it is shown that these effects are not the consequence of differences across the high- and low-load conditions in either decision noise or peripheral masking. Additionally, it is shown that of two modes of limited capacity (a limited-channel and divided-capacity model) considered as possible explanations of load effects in tasks where subjects are required to locate a target, only one--the limited-channel model--is consistent with the results from all three location tasks. Finally, it is argued that the limited-channel model predicts not only the behavior observed in the four consistent-mapping experiments reported in this article but also the behavior observed in several related consistent-mapping tasks (Kleiss & Lane, 1986; Shiffrin & Gardner, 1972).     

The Values of Counseling: Three Domains

This article examines how values, as orienting beliefs about what is good for a client, group of clients, or a nation, affect the delivery of counseling services. Specifically, this article explores the role of value assumptions within such areas as counselor-client interactions, psychometrics, career services, and the transportability of counseling theories across national boundaries.     

A developmental-genetic analysis of aggressive behavior in mice (Mus musculus): III. Behavioral mediation by heightened reactivity or immobility?

This research was designed to investigate development and behavioral mediation in lines of ICR mice that have been selectively bred for aggressive behavior. General behavioral reactivity and behavioral immobility have been implicated as potential mediators by prior analyses of preattack interactions. To evaluate the separate roles of these dispositions, the emergence of attacks in genetically selected lines was tracked for 11 years by three levels of analysis: over successive generations, over development, and over dyadic interactions. Convergent outcomes were observed in all three levels with respect to two findings: (a) Robust line differences were obtained in attack behaviors, and (b) strong associations were found between line differences in attacks and line differences in behavioral immobility. Conversely, all three levels of analysis indicated a weak and inconsistent association between line differences in attacks and measures of social and nonsocial reactivity.     

Effect of the interintromission interval on lordotic response and attack latency in golden hamsters (Mesocricetus auratus)

After 12-15 ejaculatory series, each consisting of several short intromissions (2- to 3-s vaginal penetration) and an ejaculation, male golden hamsters adopt an altered copulatory pattern consisting of long intromissions (5- to 25-s penetration with intravaginal thrusting). Receptivity declines and the tendency for the female to attack the male increases at about the time of this shift in copulatory pattern. Because the mean interintromission interval (III) between short intromissions is about 8 s compared to 100 s between long intromissions, it is possible that females detect this difference and adjust their mating accordingly. When the III between short intromissions from a rested male was experimentally increased to 100 s by use of a halter and lead device, the duration of lordosis was significantly less than that displayed by females paired with control males (8-s III) and virtually the same as that displayed by females paired with males that produced only long intromissions. This suggests that the female uses the temporal patterning of intravaginal stimulation as one criterion for terminating mating with a particular male.     

An Assessment of the Job Relevance of the National Board for Certified Counselors Examination

The authors discuss the results of a study designed to assess nationally certified counselors' perceptions of the relevance of elements of the National Board for Certified Counselors examination to their work as counselors. Support for the validity and appropriateness of the examination in regard to perceived relevance and lack of differentiation on the basis of respondent characteristics were found.     

Computerized Career Information and Guidance Systems: Caveat Emptor

Computerized career information and guidance systems, although now commonplace, have received little psychometric scrutiny. The authors argue for examining these systems in the same way in which paper and pencil instruments are assessed. Consideration is also given to issues related to programming, technical-service problems, and staffing.