Predicting and scaling hens' preferences for topographically different responses

Six hens were exposed to several concurrent (second-order) variable-interval schedules in which the response requirements on the alternatives were varied. The response requirements were one key peck versus five key pecks, one key peck versus one door push, and five key pecks versus one door push. Response- and time-allocation ratios undermatched the obtained reinforcement ratios but were well described by the generalized matching law. Time and response bias estimates from two pairs of response requirements were used to predict bias in the third pairing. The predicted values were close to those obtained; this result supports the notion that both numerically and topographically different responses act as constant sources of bias within the generalized matching law. The differences between the response and time biases could be accounted for by the different times needed to complete each response requirement. The results also suggest that the door push is a useful operant for research with domestic hens.     

The microanalysis of fixed-interval responding

The fixed-interval schedule of reinforcement is one of the more widely studied schedules in the experimental analysis of behavior and is also a common baseline for behavior pharmacology. Despite many intensive studies, the controlling variables and the pattern of behavior engendered are not well understood. The present study examined the microstructure and superstructure of the behavior engendered by a fixed-interval 5- and a fixed-interval 15-minute schedule of food reinforcement in the pigeon. Analysis of performance typical of fixed-interval responding indicated that the scalloped pattern does not result from smooth acceleration in responding, but, rather, from renewed pausing early in the interval. Individual interresponse-time (IRT) analyses provided no evidence of acceleration. There was a strong indication of alternation in shorter-longer IRTs, but these shorter-longer IRTs did not occur at random, reflecting instead a sequential dependency in successive IRTs. Furthermore, early in the interval there was a high relative frequency of short IRTs. Such a pattern of early pauses and short IRTs does not suggest behavior typical of reinforced responding as exemplified by the pattern found near the end of the interval. Thus, behavior from clearly scalloped performance can be classified into three states: postreinforcement pause, interim behavior, and terminal behavior.     

A comparison of responding maintained under second-order schedules of intramuscular cocaine injection or food presentation in squirrel monkeys.

Key pressing by squirrel monkeys was maintained under second-order schedules of either intramuscular cocaine injection or food presentation. Under one schedule, each completion of a 10-response fixed-ratio unit produced a brief visual stimulus; the first fixed-ratio unit completed after 30 minutes elapsed produced the stimulus paired with either cocaine injection or food presentation. Generally, short pauses followed by high rates of responding were maintained within the fixed-ratio units, and responding was positively accelerated over the 30-minute interval. Under another schedule, each completion of a 3-minute fixed-interval unit produced the brief stimulus; completion of the 10th fixed-interval unit produced the stimulus paired with either cocaine injection or food presentation. Generally, short pauses followed by high rates of responding were maintained within the fixed-ratio units, and responding was positively accelerated over the 30-minute interval. Under another schedule, each completion of a 3-minute fixed-interval unit produced the brief stimulus; completion of the 10th fixed-interval unit produced the stimulus paired with either cocaine injection or food presentation. Rates of responding increased within the fixed-interval units, and to a greater extent over the entire 10 fixed-interval units. Patterns of responding depended more on the schedule of reinforcement than on whether cocaine or food maintained responding. Omitting the brief stimuli following all but the last fixed-ratio or fixed-interval units decreased average rates and altered the patterns of responding. Substituting a visual stimulus that was never paired with cocaine or food following all but the last fixed-ratio or fixed-interval units decreased response rates to a lesser extent and did not substantially alter patterns of responding. When the duration of the paired stimulus was varied from .3 to 30.0 seconds, the highest response rates occurred at intermediate durations (1.0 to 10.0 seconds). The manner in which the stimulus changes affected performances depended more on the schedule of reinforcement than on whether cocaine injection or food presentation maintained responding.     

Elimination of reinforced behavior: intermittent schedules of not-responding

Pigeons' key pecking resulted in food according to either a variable-ratio or a variable-interval schedule. At the same time, food was available for not pecking for a specified time. The required time of not-pecking was segmented into not-responding units, and these units were followed by food according to a fixed-ratio schedule. Both unit duration and the number required were varied. In general, the shorter the time unit or the smaller the ratio, the lower was response rate. When total required not-responding time was constant, but changes in unit duration and the number required altered how the total was achieved, shorter units produced lower rates. Other conditions involved substitution of food delivered independent of responding for the not-responding schedule. With low and moderate total times to food presentation, the not-responding schedule produced lower rates; with the longest times, the response-independent schedule generated less responding. When considered in terms of relative frequency of food presentation available from a source other than pecking, the not-responding schedule reduced rate more effectively than did the response-independent schedule. Comparisons with other research suggested that food presented dependent on not responding compared favorably with punishment as a procedure for reducing response rate. Transient effects differed. Although punishment temporarily depresses rate when first imposed and temporarily enhances it when first removed, food given for not responding quickly generated steady-state rates.     

Fixed-interval responding under second-order schedules of food presentation or cocaine injection.

Squirrel monkeys operated a key under second-order schedules in which every tenth completion of a 5-minute fixed interval resulted in either presentation of food or intravenous injection of cocaine. When a 2-second light was presented at the completion of the component fixed-interval schedules, positively accelerated responding developed and was maintained in each component. Over a tenfold range of doses of cocaine(30 to 300 microgram/kg/injection) and amounts of food (0.75 to 7.5 g/presentation); the second-order schedule of cocaine injection maintained higher average rates of responding than the second-order schedule of food presentation. Substituting saline for cocaine or eliminating food presentation decreased average rates of responding. When no stimulus change occurred at the completion of the first nine component fixed-interval schedules, but the 2-second light and food presentation or cocaine injection still occurred after the tenth component, only low and relatively constant rates of responding were maintained in each component. Patterns of responding characteristic of 5-minute fixed-interval schedules were maintained by the 2-second light paired with either cocaine injection or food presentation, though the maximum frequency of cocaine injection or food presentation was less than once per 50 minutes.     

On the Consistency of the Δ1 1-CA Fragment of Frege's Grundgesetze

It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing ¹ ₁-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

The Counseling Center Assessment of Psychological Symptoms Distress Index: A pragmatic exploration of general factors to enhance a multidimensional scale

Objective: The authors attempted to develop and validate a general distress index for a multidimensional psychological symptom/outcome measure used in over 300 college counseling centers with more than 100,000 cases annually: the Counseling Center Assessment of Psychological Symptoms (CCAPS). Method: Four models were compared for fit indices (n = 19,247): the existing first-order factor model (without a general factor), a second-order factor model, a bifactor model, and a single factor or “total score” model. In separate clinical and non-clinical samples, concurrent and divergent validity were examined using several well-established measures of psychological symptoms, as well as two-week test–retest and treatment utilization data. Results: Second-order and bifactor models which captured a single “distress” factor both exhibited good fit to the data relative to the baseline and “total score” model. Validity data indicated that factors adequately measured meaningful clinical onstructs. Conclusion: Both the bifactor and second-order models indicated the presence of a “distress index” comprised items across many of the CCAPS subscales. This distress scale has strong applicability for benchmarking the overall severity and complexity of patients at different centers, and can be used to help identify colleges and universities with areas of clinical strength, which can be studied to improve the field. Clinically, the distress index offers a parsimonious and efficient method for clinicians to monitor patients’ progress through treatment.     

Life of the Second-Order Patient: Factors Impacting the Informal Caregiver

Informal caregivers (ICs) are forced to make adaptive lifestyle changes to meet the significant demand of caring for loved ones who are terminally ill. Open-ended questions were administered with 26 ICs who cared for loved ones diagnosed with terminal illnesses whose prognosis was less than six months. The results add substantive information to parsimonious literature and demonstrate a correlation with existing studies that coincide with the debilitating effects that caregiving has on the informal carer. The study clarifies the complexities of the caregiving role characterized by the involvement that may adversely affect socialization, physical health conditions, and marital dynamics, among other areas of the IC’s personal life.     

A General Setting for Dedekind's Axiomatization of the Positive Integers

A Dedekind algebra is an ordered pair (B, h), where B is a non-empty set and h is a similarity transformation on B. Among the Dedekind algebras is the sequence of the positive integers. From a contemporary perspective, Dedekind established that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. The purpose here is to show that this seemingly isolated result is a consequence of more general results in the model theory of second-order languages. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are ?₀ isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on ω called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type that occurs in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. The second-order theory of any countably infinite Dedekind algebra is categorical, and there are countably infinite Dedekind algebras whose second-order theories are not finitely axiomatizable. It is shown that there is a condition on configuration signatures necessary and sufficient for the second-order theory of a Dedekind algebra to be finitely axiomatizable. It follows that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable.