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.     

Nonverbal communication as a compensative strategy for severely nonfluent aphasics? A quantitative approach

Seven severely nonfluent aphasics and one relative or close friend were investigated in an interview situation. The conversation was videotaped and analyzed for the use of nonverbal communication between aphasic and partner. The results indicate that the group of aphasics used significantly more frequently and for a significantly longer period of time nonverbal channels of communication than their healthy partners. The aphasic patients also used significantly fewer speech-focused movements and significantly more codified gestures. Nonverbal elements were more frequently used as speech substitutes by the group of aphasics.     

Role of the area postrema in three putative measures of motion sickness in the rat

After thermal cauterization of the area postrema in rats the absence of conditioned taste aversion to sucrose paired with lithium chloride (0.15 M, 3.3 ml/kg) was used as a pharmacologic/behavioral index of area postrema damage. In a subsequent experiment the effects of area postrema lesions on three measures proposed as species-relevant measures of motion sickness were studied, using off-vertical rotation at 150 degrees/s for either 30 or 90 min. Lesions of area postrema did not alter postrotational suppression of drinking or amount of defecation during motion. The initial acquisition of conditioned taste aversion to a novel cider vinegar solution paired with motion was not affected by lesioning of the area postrema, but these taste aversions extinguished more slowly in lesioned rats than in sham-operates or intact controls. Results are discussed in terms of proposed humoral factors which may induce motion sickness and in light of recent data on the role of the area postrema in similar measures in species possessing the complete emetic reflex.     

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.     

Academic achievement and attributions among college students: Effects of gender and sex typing

Attribution questionnaires were completed by 137 students in an introductory economics course immediately preceding the first exam in their class and immediately after their exams were returned. Results indicate that males and females used attributions differently, although not as a function of perceived outcome. In contrast, sex-typing groups varied their attribution as a function of perceived outcome. Self-esteem is proposed as a possible mediating variable. It was concluded that sex typing in relation to perceived successful and unsuccessful performance is an important variable in attributional research.     

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.