Probability Relations within Response Sequences under Ratio Reinforcement.
01 Apr 1958-Journal of the Experimental Analysis of Behavior (Society for the Experimental Analysis of Behavior)-Vol. 1, Iss: 2, pp 109-121
About: This article is published in Journal of the Experimental Analysis of Behavior.The article was published on 1958-04-01 and is currently open access. It has received 264 citations till now. The article focuses on the topics: Reinforcement.
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TL;DR: In this paper, a consistent vocabulary and theoretical framework for evaluating numerical competence in animals is proposed, where relative numerousness judgments, subitizing, counting, and estimation may be the essential processes by which animals perform numerical discriminations.
Abstract: Numerical competence is one of the many aspects of animal cognition that have enjoyed a resurgence of interest during the past decade. Evidence for numerical abilities in animals has followed a tortuous path to respectability, however, from Clever Hans, the counting horse, to modern experimental studies. Recent surveys of the literaturereveal theoretical as well as definitional confusion arising from inconsistent terminology for numerical processes and procedures. The term “counting” has been applied to situations having little to do with its meaning in the human literature. We propose a consistent vocabulary and theoretical framework for evaluating numerical competence. Relative numerousness judgments, subitizing, counting, and estimation may be the essential processes by which animals perform numerical discriminations. Ordinality, cardinality, and transitivity also play an important role in these processes. Our schema is applied to a variety of recent experimental situations. Some evidence of transfer is essential in demonstrating higher-order ability such as counting or “sense of number.” Those instances of numerical competence in which all viable alternatives to counting (e.g., subitizing) have been precluded, but no evidence of transfer has been demonstrated might be described as “protocounting.” To show that animals are capable of “true” counting future research will have to demonstrate generality across situations.
451 citations
TL;DR: Neural representations of numerical information can engage extensive cerebral networks, but the posterior parietal cortex and the prefrontal cortex are the key structures in primates.
Abstract: Numbers are an integral part of our everyday life - we use them to quantify, rank and identify objects. The verbal number concept allows humans to develop superior mathematical and logic skills that define technologically advanced cultures. However, basic numerical competence is rooted in biological primitives that can be explored in animals, infants and human adults alike. We are now beginning to unravel its anatomical basis and neuronal mechanisms on many levels, down to its single neuron correlate. Neural representations of numerical information can engage extensive cerebral networks, but the posterior parietal cortex and the prefrontal cortex are the key structures in primates.
433 citations
Cites background from "Probability Relations within Respon..."
...Two general effects that are seen in analogue magnitude representations are the numerical distance effect (discrimination between two cardinalities improves with increasing numerical distance between them) and the numerical magnitude effect (discrimination of two numerosities of a given numerical distance becomes more difficult as the absolute values of the two sets get higher...
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TL;DR: By bringing together knowledge from different areas of research it is hoped that a cross fertilization will be achieved, which will lead to a sharpening of concepts, an improvement in methodology and the stimulation of biological studies.
Abstract: Impulsivity can often be an important clinical problem in psychiatry and neurology. In psychiatry, the manifestation of impulsive behaviour in syndromes such as personality disorders, attention deficit hyperactivity disorder and in substance abuse may be different, and this has led to conflicting definitions. There has also been a tendency to concentrate on the nature of the behavioural manifestation (problems with the law, aggression, drug use, behavioural problems in school) rather than shared psychological processes, and to ignore the fact that impulsivity can also have positive aspects. In a normal population, the personality trait of impulsivity has been analysed using personality inventory questionnaires. Analysis of these data lead to the suggestion that impulsivity as commonly defined and understood may be made up of several independent factors, which may have separate biological bases. These self-rating questionnaires have been complemented by objective tests that are now often computerized, and which have been used in man (e.g. with criminal offenders, children, or patients who have undergone brain surgery). Some of these tests, such as the differential reinforcement of low rates procedure or the delay of reinforcement procedure, have also been used to study impulsivity in animals. Analysis of the behavioural principles of these tests suggests that they too may reflect different aspects of impulsivity. Many different biological systems have been proposed to contribute to the neurobiological basis of impulsivity. The serotonergic neurotransmitter system has recently received the most attention, with evidence of its involvement coming from animal studies as well as from studies in psychiatric patients. The frontal lobes have been proposed to play an important role in regulating impulsivity, although it unclear how specific this is. None of this biological knowledge has yet led to reliable pharmacotherapy for excessive impulsivity and, as yet, there is little understanding of the mechanisms by which those drugs, which have been found empirically to have some efficacy (e.g. the psychomotor stimulants in attention deficit hyperactivity disorder), exert their therapeutic effect. By bringing together knowledge from different areas of research it is hoped that a cross fertilization will be achieved, which will lead to a sharpening of concepts, an improvement in methodology and the stimulation of biological studies.
413 citations
TL;DR: Collectively these studies show that monkeys represent the numerosities 1-9 on at least an ordinal scale.
Abstract: Three rhesus monkeys (Macaca mulatta) were trained to respond to exemplars of 1, 2, 3, and 4 in an ascending, descending, or a nonmonotonic numerical order (1-->2-->3-->4, 4-->3-->2--1, 3-->1-->4-->2). The monkeys were then tested on their ability to order pairs of the novel numerosities 5-9. In Experiment 1, all 3 monkeys ordered novel exemplars of the numerosities 1-4 in ascending or descending order. The attempt to train a nonmonotonic order (3-->1-->4-->2) failed. In Experiment 2A, the 2 monkeys who learned the ascending numerical rule ordered pairs of the novel numerosities 5-9 on unreinforced trials. The monkey who learned the descending numerical rule failed to extrapolate the descending rule to new numerosities. In Experiment 2B all 3 monkeys ordered novel exemplars of pairs of the numerosities 5-9. Accuracy and latency of responding revealed distance and magnitude effects analogous to previous findings with human participants (R. S. Moyer & T. K. Landaeur, 1967). Collectively these studies show that monkeys represent the numerosities 1-9 on at least an ordinal scale.
257 citations
Additional excerpts
..., Davis, 1984; Emmerton, Lohmann, & Niemann, 1997; Hicks, 1956; Honig & Stewart, 1989; Thomas, Fowlkes, & Vickery, 1980), the number of responses to a manipulandum (Fetterman, 1993; Mechner, 1958; Platt & Johnson, 1971;RiUing, 1967), and the number of reinforcers (Olthof, Iden, & Roberts, 1997; Washburn & Rumbaugh, 1991)....
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TL;DR: In this article, the authors use the slopes of learning curves to infer which response comes closest to the organism's definition of the response, and the resulting exponentially weighted moving average provides a model of memory that is used to ground a quantitative theory of reinforcement, where incentives excite behavior and focus the excitement on responses that are contemporaneous in memory.
Abstract: Effective conditioning requires a correlation between the experimenter's definition of a response and an organism's, but an animal's perception of its behavior differs from ours. These experiments explore various definitions of the response, using the slopes of learning curves to infer which comes closest to the organism's definition. The resulting exponentially weighted moving average provides a model of memory that is used to ground a quantitative theory of reinforcement. The theory assumes that: incentives excite behavior and focus the excitement on responses that are contemporaneous in memory. The correlation between the organism's memory and the behavior measured by the experimenter is given by coupling coefficients, which are derived for various schedules of reinforcement. The coupling coefficients for simple schedules may be concatenated to predict the effects of complex schedules. The coefficients are inserted into a generic model of arousal and temporal constraint to predict response rates under any scheduling arrangement. The theory posits a response-indexed decay of memory, not a time-indexed one. It requires that incentives displace memory for the responses that occur before them, and may truncate the representation of the response that brings them about. As a contiguity-weighted correlation model, it bridges opposing views of the reinforcement process. By placing the short-term memory of behavior in so central a role, it provides a behavioral account of a key cognitive process.
250 citations
References
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TL;DR: I am indebted to Professor Lighthill for some further illuminating remarks regarding this point and his comments on Heisenberg's Theory of Isotropic Turbulence are highly illuminating.
Abstract: 1 G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge: At the University Press, 1954). 2 G. K. Batchelor and A. A. Townsend, \"Decay of Turbulence in the Final Period of Decay,\" Proc. Roy. Soc. London, A, 194, 527-543, 1948. 3 W. Heisenberg, \"Zur statistischen Theorie der Turbulenz,\" Z. Physik, 124, 628-657, 1948. 4W. H. Reid, \"Two Remarks on Heisenberg's Theory of Isotropic Turbulence,\" Quart. Appl. Math. 14, 201-205, 1956. 6 Cf. M. J. Lighthill, Nature, 173, 746, 1954. I am indebted to Professor Lighthill for some further illuminating remarks regarding this point.
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