Achievement-oriented and dependency-oriented parental psychological control: An examination of specificity to middle childhood achievement and dependency-related problems

Middle childhood is considered a sensitive phase for the development of both dependency and achievement-related problems. In order to target efficient prevention and treatment, it is necessary to identify unique associations with possible precursors. This study hypothesized that children’s dependency-related problems (i.e., separation anxiety and generalized anxiety) would uniquely relate to parental dependency-oriented psychological control and that children’s achievement-related problems (i.e., extrinsic motivation and maladaptive perfectionism) would uniquely relate to parental achievement-oriented psychological control. The study included 180 elementary school children. Results showed that higher levels of children’s separation anxiety uniquely related to more parental dependency-oriented psychological control, while higher levels of children’s extrinsic motivation uniquely related to more parental achievement-oriented psychological control. Contrary to the expectations, higher levels of children’s maladaptive perfectionism were associated with both dimensions of parental psychological control, and children’s generalized anxiety was not associated with any dimension. Study implications are discussed.     

On Ultrafilter Logic and Special Functions

Logics for generally were introduced for handling assertions with vague notions,such as generally, most, several, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.Presented by André Fuhrmann     

Earning and obtaining reinforcers under concurrent interval scheduling

Contingencies of reinforcement specify how reinforcers are earned and how they are obtained. Ratio contingencies specify the number of responses that earn a reinforcer, and the response satisfying the ratio requirement obtains the earned reinforcer. Simple interval schedules specify that a certain time earns a reinforcer, which is obtained by the first response after the interval. The earning of reinforcers has been overlooked, perhaps because simple schedules confound the rates of earning reinforcers with the rates of obtaining reinforcers. In concurrent variable-interval schedules, however, spending time at one alternative earns reinforcers not only at that alternative, but at the other alternative as well. Reinforcers earned for delivery at the other alternative are obtained after changing over. Thus the rates of earning reinforcers are not confounded with the rate of obtaining reinforcers, but the rates of earning reinforcers are the same at both alternatives, which masks their possibly differing effects on preference. Two experiments examined the separate effects of earning reinforcers and of obtaining reinforcers on preference by using concurrent interval schedules composed of two pairs of stay and switch schedules (MacDonall, 2000). In both experiments, the generalized matching law, which is based on rates of obtaining reinforcers, described responding only when rates of earning reinforcers were the same at each alternative. An equation that included both the ratio of the rates of obtaining reinforcers and the ratio of the rates of earning reinforcers described the results from all conditions from each experiment.     

Choice in a variable environment: effects of unequal reinforcer distributions

Six pigeons were trained in a procedure in which sessions included seven unsignaled components, each offering two pecking keys, and each providing a potentially different reinforcer ratio between the two keys. Across conditions, various combinations of reinforcer ratios and reinforcer-magnitude ratios were used to create unequal reinforcer distributions between the two alternatives when averaged across a session. The results extended previous research using the same basic procedure that had included only reinforcer distributions symmetrical around 1:1. Data analyses suggested that the variables controlling choice operated at a number of levels: First, individual reinforcers had local effects on choice; second, sequences of successive reinforcers obtained at the same alternative (continuations) had cumulative effects; and, third, when these sequences themselves occurred with greater frequency, their effects further cumulated. A reinforcer obtained at the other alternative following a sequence of continuations (a discontinuation) had a large effect and apparently reset choice to levels approximating the sessional reinforcer ratio.     

Concurrent-schedule performance in transition: changeover delays and signaled reinforcer ratios

Six pigeons were trained in experimental sessions that arranged six or seven components with various concurrent-schedule reinforcer ratios associated with each. The order of the components was determined randomly without replacement. Components lasted until the pigeons had received 10 reinforcers, and were separated by 10-s blackout periods. The component reinforcer ratios arranged in most conditions were 27:1, 9:1, 3:1, 1:1, 1:3, 1:9 and 1:27; in others, there were only six components, three of 27:1 and three of 1:27. In some conditions, each reinforcement ratio was signaled by a different red-yellow flash frequency, with the frequency perfectly correlated with the reinforcer ratio. Additionally, a changeover delay was arranged in some conditions, and no changeover delay in others. When component reinforcer ratios were signaled, sensitivity to reinforcement values increased from around 0.40 before the first reinforcer in a component to around 0.80 before the 10th reinforcer. When reinforcer ratios were not signaled, sensitivities typically increased from zero to around 0.40. Sensitivity to reinforcement was around 0.20 lower in no-changeover-delay conditions than in changeover-delay conditions, but increased in the former after exposure to changeover delays. Local analyses showed that preference was extreme towards the reinforced alternative for the first 25 s after reinforcement in changeover-delay conditions regardless of whether components were signaled or not. In no-changeover-delay conditions, preference following reinforcers was either absent, or, following exposure to changeover delays, small. Reinforcers have both local and long-term effects on preference. The former, but not the latter, is strongly affected by the presence of a changeover delay. Stimulus control may be more closely associated with longer-term, more molar, reinforcer effects.     

Every reinforcer counts: reinforcer magnitude and local preference

Six pigeons were trained on concurrent variable-interval schedules. Sessions consisted of seven components, each lasting 10 reinforcers, with the conditions of reinforcement differing between components. The component sequence was randomly selected without replacement. In Experiment 1, the concurrent-schedule reinforcer ratios in components were all equal to 1.0, but across components reinforcer-magnitude ratios varied from 1:7 through 7:1. Three different overall reinforcer rates were arranged across conditions. In Experiment 2, the reinforcer-rate ratios varied across components from 27:1 to 1:27, and the reinforcer-magnitude ratios for each alternative were changed across conditions from 1:7 to 7:1. The results of Experiment 1 replicated the results for changing reinforcer-rate ratios across components reported by Davison and Baum (2000, 2002): Sensitivity to reinforcer-magnitude ratios increased with increasing numbers of reinforcers in components. Sensitivity to magnitude ratio, however, fell short of sensitivity to reinforcer-rate ratio. The degree of carryover from component to component depended on the reinforcer rate. Larger reinforcers produced larger and longer postreinforcer preference pulses than did smaller reinforcers. Similar results were found in Experiment 2, except that sensitivity to reinforcer magnitude was considerably higher and was greater for magnitudes that differed more from one another. Visit durations following reinforcers measured either as number of responses emitted or time spent responding before a changeover were longer following larger than following smaller reinforcers, and were longer following sequences of same reinforcers than following other sequences. The results add to the growing body of research that informs model building at local levels.     

Choice, contingency discrimination, and foraging theory

Four pigeons were trained on eight or nine pairs of independent concurrent variable-interval schedules. The range of reinforcement ratios included extreme ratios (up to 532 to 1). Large samples of stable performance were gathered. Contrary to the findings of Davison and Jones (1995), the generalized matching law described choice more accurately than a contingency-discriminability model. Taking small samples (5 to 10 sessions) and applying a more liberal stability criterion used by Davison and Jones only increased the unsystematic variance in the data and in estimates of generalized-matching-law sensitivity. Because changing to dependent scheduling and inserting a changeover delay had no systematic effect, the deviations from generalized matching reported by Davison and Jones probably arose from imperfectly discriminated stimuli. Analysis of visits revealed that visits to the nonpreferred alternative were brief and approximately constant. When choice between the preferred (rich) and nonpreferred (lean) alternatives, regardless of position, was analyzed according to the generalized matching law, sensitivities approximated 1.0, with bias in favor of the lean alternative. This bias, which arose from an excessive frequency of visits to the lean alternative, explains undermatching as the result of fitting one line to a choice relation that consists of two displaced lines, both with a slope of 1.0. The pattern of deviation from the generalized matching line confirmed this account. The findings suggest an alternative analysis of choice that focuses on probability of visiting the lean alternative as the dependent variable. This probability was directly proportional to ratio of reinforcement. Matching, undermatching, and overmatching may all be explained by a view of concurrent performance based on foraging theory, in which responding occurs primarily at the rich alternative and is occasionally interrupted by brief visits to the lean alternative.     

Quantifiers and Congruence Closure

We prove some results about the limitations of the expressive power of quantifiers on finite structures. We define the concept of a bounded quantifier and prove that every relativizing quantifier which is bounded is already first-order definable (Theorem 3.8). We weaken the concept of congruence closed (see [6]) to weakly congruence closed by restricting to congruence relations where all classes have the same size. Adapting the concept of a thin quantifier (Caicedo [1]) to the framework of finite structures, we define the concept of a meager quantifier. We show that no proper extension of first-order logic by means of meager quantifiers is weakly congruence closed (Theorem 4.9). We prove the failure of the full congruence closure property for logics which extend first-order logic by means of meager quantifiers, arbitrary monadic quantifiers, and the Härtig quantifier (Theorem 6.1).     

Partially Interpreted Relations and Partially Interpreted Quantifiers

Logics in which a relation R is semantically incomplete in a particular universe E, i.e. the union of the extension of R with its anti-extension does not exhaust the whole universe E, have been studied quite extensively in the last years. (Cf. van Benthem (1985), Blamey (1986), and Langholm (1988), for partial predicate logic; Muskens (1996), for the applications of partial predicates to formal semantics, and Doherty (1996) for applications to modal logic.) This is not so with semantically incomplete generalized quantifiers which constitute the subject of the present paper. The only systematic study of these quantifiers from a purely logical point of view, is, to the best of my knowledge, that by van Eijck (1995). We shall take here a different approach than that of van Eijck and mention some of the abstract properties of the resulting logic. Finally we shall prove that the two approaches are interdefinable.     

Matching under nonindependent variable-ratio schedules of drug reinforcement.

Response-contingent deliveries of oral pentobarbital maintained responding of 3 rhesus monkeys during daily 3-hr sessions. Deliveries of pentobarbital were arranged under nonindependent concurrent variable-ratio variable-ratio schedules. Responses to either schedule counted toward completion of both variable-ratio schedule requirements. This schedule is similar in some respects to conventional concurrent variable-interval variable-interval schedules, in which passage of time counts toward completion of the interval value on both schedules. Restricted nonindependent concurrent variable-ratio variable-ratio schedules were also studied. On that schedule, when a drug delivery was assigned to one spout, it had to be collected before responses on the opposite spout again counted toward completion of the schedule requirements. Relative reinforcer magnitude was varied by changing the drug concentration on one schedule while keeping the drug concentration constant on the other variable-ratio schedule. Under both types of concurrent variable-ratio schedules, the relative rate of responding corresponded to the relative drug intake. Unlike earlier studies of concurrent variable-interval variable-interval intravenous cocaine reinforcement, preference was proportionate to concentration, and exclusive preferences did not develop. The relationship between relative rate of responding and relative drug intake was well described by the generalized matching law.