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.     

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.     

Multiunit changes in hippocampus and medial geniculate body in free-behaving rats during acquisition and retention of a conditioned response to a tone

Multiunit activity (MUA) was recorded chronically in the hippocampus (CA3) and the medial geniculate body (mMG) during habituation to a tone followed by conditioning (tone paired with footshock) or pseudoconditioning (tone/footshock unpaired) in rats previously trained in a lever-pressing for food task (VI 60). In the conditioned group pairing tones with footshocks rapidly induced an increase in the initial CS-evoked response in the mMG, followed by the emergence of a hippocampal response and a marked conditioned suppression of lever-pressing to the tone. In contrast, in the pseudoconditioned group, the stimulus induced only transient cellular changes in the hippocampus and in the mMG, while no behavioral suppression to the tone could be seen. Moreover, presentations of the CS 45 days later induced multiunit and behavioral responses in both structures, only in the conditioned group. These results are used for discussion of the role of learning-induced changes in the sensory structure (mMG) as compared with changes in an associative structure (hippocampus), during acquisition and retention of a conditioned response.     

Is it smart to play the horses? Comment on "A day at the races: a study of IQ, expertise, and cognitive complexity" (Ceci & Liker, 1986)

Ceci and Liker (1986b) presented data that they contended shows two things: (a) Handicapping harness races is a cognitively complex undertaking that can be captured by a multiple regression model, and (b) neither overall skill at handicapping nor the complexity of the mental model used is related to standard measures of intelligence. The first contention is not at issue. But the second contention, that handicapping performance is unrelated to IQ, is not supported by the data presented; in fact, the opposite conclusion seems more likely. The purpose of this comment is to point out errors frequently made in individual-differences research concerning population definition, sample selection, dependent and independent variable reliability and validity and interpretation of results.     

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)     

Chronic sweet intake lowers pain thresholds without changing brain mu- or delta-opiate receptors

Sprague-Dawley rats drank sweetened (3% dextrose + 0.144% saccharin, w/v) or unflavored water for 18 days and subsequent pain reactivity was assessed using a hot plate. Compared to the rats that consumed unflavored water, the rats that consumed sweet water responded more quickly on the hot plate indicating that their threshold for pain was lowered. Another group of rats given identical exposure to the fluids had their brains prepared for measuring opiate receptor binding using the delta-receptor ligand [3H]D-Ala-D-Leu-enkephalin ([3H]DADLE) and the mu-receptor selective ligand [3H]Tyr-D-Ala-Gly-MePhe-Gly-ol ([ 3H]DAGO). Binding of these opiates to mu- and delta-receptors in the cerebral cortex, striatum, hippocampus, hypothalamus, brain stem, and remaining brain regions was the same for the rats that drank sweet fluids and those that drank unflavored water. These findings suggest that drinking sweet fluids lowers pain thresholds but does not alter mu- and delta-receptors.     

Effects of aging and task difficulty on divided attention performance

We report two experiments that compare the performance of young and older adults on perceptual-motor tasks involving division of attention. Previous studies have shown older people to be especially penalized by divided attention situations, but the generality of this finding was recently challenged by Somberg and Salthouse (1982). The present study was conducted to investigate the possibility that age differences in dual-task performance are amplified by an increase in the difficulty of the constituent tasks, where difficulty was manipulated by varying the central, cognitive nature of the tasks (Experiment 1) or the degree of choice involved (Experiment 2). With the present tasks, strong evidence was found for an age-related decrement in divided attention performance. Contrary to our original expectations, however, it does not seem that division of attention presents some especial difficulty to older people. Rather, division of attention is one of several equivalent ways to increase overall task complexity. In turn, age differences are exaggerated as tasks are made more complex.     

Representation of serial order in monkeys (Cebus apella)

Cebus monkeys were trained on a five-item serial learning task, symbolized as ABCDE; the initial stages of training were on the shorter subseries AB, ABC, and ABCD. To assess the monkeys' knowledge of the sequential position of each item, pair-wise tests were given to 2 subjects after acquisition of the ABCD series and to 4 subjects after reaching criterion on the ABCDE series. In both tests, the monkeys performed at high levels on the interior pairs, which were BC for the ABCD series, and BC, BD, and CD for the ABCDE series. These results, as well as the orderly relations observed in the pair-wise tests between first-item response latency and first-item position and between second-item response latency and number of missing items, indicated that the monkeys had developed a well-organized internal representation of the four- and five-item series. Although pigeons are also capable of learning four-item and five-item series, they apparently do not develop a comparable representational structure. The disparity between the monkeys' and pigeons' representational competence for serial order is predictable from the difference in their capacities for associative transitivity.     

Affective state mediates causal attributions for success and failure

The influence of affect on causal attributions for success and failure was examined in this experiment. A positive, neurtral, or negative mood was induced in subjects who then learned they had either succeeded or failed an aptitude test taken previously. Relative to neutral mood control conditions, subjects in both positive and negative mood conditions showed a pronounced self-serving bias, particularly following success. The finding is interpreted as self-regulation of affective state. Specifically, causal attribution of success to internal factors can sustain or enhance positive affect; attribution of failure to external factors can diminish negative affect. Ancillary analyses corroborated this interpretation.