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.     

Fuzziness of concepts and concepts of fuzziness

It has been a vexing question in recent years whether concepts are fuzzy. In this paper several views on the fuzziness of concepts are pointed out to have stemmed from dubious concepts of fuzziness. The underlying notions of the roles feasibly played byprototype, set, andprobability in modeling concepts strongly suggest that the controversy originates from a vague relation between intuitive and mathematical ideas in the cognitive sciences. It is argued that the application of fuzzy sets cannot resolve this vagueness since they are one sided,viz., defined on sets. An alternative definition based on classes (in the sense of axiomatic set theory) is proposed.     

Perceptions of speakers with minimal eye contact: Implications for stutterers

One hundred and thirty-three college students responded to percentage definitions of “good,” “minimal,” and “no” eye contact. They also judged their perceptions of a speaker with “little or no eye contact” on a semantic differential scale containing 60 polarized adjective pairs regarding personality traits. The majority of the student respondents defined an individual with “good” eye contact as looking at his/her audience/listener 90–100% of the time. This is a more stringent definition than other literature has indicated. Furthermore, speakers with little or no eye contact were judged less favorably on 70% of the items, which indicates that low eye contact adversely affects perceptions of a speaker's personality. Therefore, stutterers need to be made aware of the importance of and determinants of effective eye contact in communication. Also, the development of effective eye contact needs to be incorporated as a major goal in stuttering therapy.     

Stress in time

The goals of this research were to determine whether speakers adjust the stress patterns of words within sentences to create an alternation between strong and weak beats and to explore whether this rhythmic alternation contributes to the characteristics stress differences between two major lexical categories of English. Two experiments suggested that speakers do alter lexical stress in accordance with rhythmic biases. When speakers produced disyllabic pseudowords in sentence contexts, they were more likely to place stress on the first syllable when the pseudoword was preceded by a weak stress and followed by a strong one than when the strong stress preceded and the weak followed. This occurred both when the pseudowords served as nouns and when they served as verbs. Text analyses further revealed that weakly stressed elements precede nouns more often than verbs, whereas such elements follow verbs more often than nouns. Thus, disyllabic nouns are more likely than disyllabic verbs to occupy contexts biased toward trochaic rhythm, a finding consistent with leftward dominant stress in disyllabic English nouns. The history of stress changes in English nouns and verbs also conforms with the view that rhythmic context may have contributed to the evolution of stress differences. Together, the findings suggest that the citation stress patterns of words may to some degree reflect adaptations of lexical knowledge to conditions of language performance.     

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.     

Isolation-dependent enhancement of 2-[14C]deoxyglucose uptake in the forebrain of zebra finch males

In a previous study (H. J. Bischof & K. Herrmann (1986), Behavioral Brain Research, 21, 215-221) we demonstrated that four forebrain areas of the zebra finch male are activated in situations which arouse the animal, for example when the birds are chased around the cage or when they are exposed to a female. These areas, the hyperstriatum accessorium-dorsale (HAD), a part of the medial neo-hyperstriatum (MNH), the lateral neo-hyperstriatum (LNH), and a portion of the caudal archi-neostriatum (ANC), show enhanced 2-[14C]deoxyglucose (2-DG) uptake according to the experimental situation. On the basis of these experiments, we examined whether the activation of the areas is correlated with motor activity and is influenced by different isolation times prior to a 2-DG experiment, where courtship of the male birds is elicited by exposing them to a female zebra finch. For this purpose, we isolated male zebra finches for 1 day, 1 week, or 8 weeks, respectively, before we injected the 2-DG and exposed the birds to a female. During the experiment, besides other activities, the number of song motifs performed by the bird and the frequency of changing perches was recorded. Our experiments demonstrate that there is a weak negative correlation between motor activity and 2-DG uptake, and a positive correlation between isolation time and 2-DG uptake. We suggest that long isolation blocks courtship behavior by some unknown mechanisms, and that the "internal drive" of the animal, which possibly corresponds with the activity of the four forebrain areas, is enhanced by isolation and by the fact that the birds do not perform the consummatory behavior. Our results also demonstrate that the 2-DG method can show up small differences in the internal state of an animal, which cannot easily be detected by behavioral measurements.     

Selective attention: effects of cuing on the processing of different types of compound stimuli

Pigeons in a matching-to-sample experiment received (a) element samples (one of two colors or vertical or horizontal white lines), (b) separated compound samples (a color and a line element presented together), and (c) unified compound samples (vertical or horizontal colored lines). In Phase I, test stimuli were the two elements from one dimension; the dimension tested varied randomly when the sample was a compound. Element samples were matched better than unified samples, which were matched better than separated samples. In Phase II, two samples preceded the tests. On EC trials, the first sample (S1) was an element, and the second sample (S2) was a compound; on CE trials this order was reversed. One element of the compound sample was always the one appearing as the element sample on that trial (e.g., S1 = red, S2 = red-vertical). This element also served as the correct test alternative (e.g., test = red+ vs. green) except on probe trials when the correct test was the other element appearing in the compound (e.g., test = vertical+ vs. horizontal). Accuracy varied as a function of sample sequence when the compound was separated (EC greater than CE on nonprobe trials and CE greater than EC on prove trials). This pattern was not observed when the compound was unified. The data suggest that the element in EC trials served as a cue that increased processing of the cued dimension and decreased processing of the noncued dimension of separated compounds. However, both dimensions of unified compounds seem to have been processed regardless of cuing.(ABSTRACT TRUNCATED AT 250 WORDS)