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In the Mid-Session Reversal task (MSR), an animal chooses between two options, S1 and S2. Rewards follow S1 but not S2 from trials 1-40, and S2 but not S1 from trials 41-80. With pigeons, the psychometric function relating S1 choice proportion to trial number starts close to 1 and ends close to 0, with indifference (PSE) close to trial 40. Surprisingly, pigeons make anticipatory errors, choosing S2 before trial 41, and perseverative errors, choosing S1 after trial 40. These errors suggest that they use time into the session as the preference reversal cue. We tested this timing hypothesis with 10 Spotless starlings. After learning the MSR task with a T-s Inter-Trial Interval (ITI), they were exposed to either 2 T or T/2 ITIs during testing. Doubling the ITI should shift the psychometric function to the left and halve its PSE, whereas halving the ITI should shift the function to the right and double its PSE. When the starlings received one pellet per reward, the ITI manipulation was effective: The psychometric functions shifted in the direction and by the amount predicted by the timing hypothesis. However, non-temporal cues also influenced choice. published

Eckard and Lattal (2020) summarized the behavioristic view of hypothetical constructs and theories, and then, in a novel and timely manner, applied this view to a critique of internal clock models of temporal control. In our three-part commentary, we aim to contribute to the authors’ discussion by first expanding upon their view of the positive contributions afforded by constructs and theories. We then refine and question their view of the perils of reifying constructs and assigning them causal properties. Finally, we suggest to behavior analysts four rules of conduct for dealing with mediational theories: tolerate constructs proposed with sufficient reason; consider them seriously, both empirically and conceptually; develop alternative, behavior-analytic models with overlapping empirical domains; and contrast the various models. Through variation and selection, behavioral science will evolve.

Researchers have unraveled multiple cases in which behavior deviates from rationality principles. We propose that such deviations are valuable tools to understand the adaptive significance of the underpinning mechanisms. To illustrate, we discuss in detail an experimental protocol in which animals systematically incur substantial foraging losses by preferring a lean but informative option over a rich but non-informative one. To understand how adaptive mechanisms may fail to maximize food intake, we review a model inspired by optimal foraging principles that reconciles sub-optimal choice with the view that current behavioral mechanisms were pruned by the optimizing action of natural selection. To move beyond retrospective speculation, we then review critical tests of the model, regarding both its assumptions and its (sometimes counterintuitive) predictions, all of which have been upheld. The overall contention is that (a) known mechanisms can be used to develop better ultimate accounts and that (b) to understand why mechanisms that generate suboptimal behavior evolved, we need to consider their adaptive value in the animal’s characteristic ecology.

When offered a choice between 2 alternatives, animals sometimes prefer the option yielding less food. For instance, pigeons and starlings prefer an option that on 20% of the trials presents a stimulus always followed by food, and on the remaining 80% of the trials presents a stimulus never followed by food (the Informative Option), over an option that provides food on 50% of the trials regardless of the stimulus presented (the Noninformative Option). To explain this suboptimal behavior, it has been hypothesized that animals ignore (or do not engage with) the stimulus that is never followed by food in the Informative Option. To assess when pigeons attend to the stimulus usually not followed by food, we increased the probability of reinforcement, p, in the presence of that stimulus. Across 2 experiments, we found that the value of the Informative Option decreased with p. To account for the results, we added to the Reinforcement Rate Model (and also to the Hyperbolic Discounting Model) an engagement function, f(p), that specified the likelihood the animal attends to a stimulus followed by reward with probability p, and then derived the model predictions for 2 forms of f(p), a linear function, and an all-or-none threshold function. Both models predicted the observed findings with a linear engagement function: The higher the probability of reinforcement after a stimulus, the higher the probability of engaging the stimulus, and, surprisingly, the less the value of the option comprising the stimulus., This study was conducted at the Psychology Research Centre (UID/PSI/01662/2013) of the University of Minho, and supported by the Portuguese Foundation for Science and Technology (FCT) and the Portuguese Ministry of Science, Technology and Higher Education through national funds and cofinanced by FEDER through COMPETE2020 under the PT2020 Partnership Agreement (POCI-01-0145-FEDER-007653). This work was also supported by an FCT Grant (PTDC/MHC-PCN/3540/2012) to AM. IF and CP were supported by FCT Doctoral Grants (SFRH/BD/77061/2011 and SFRH/BD/78566/2011, respectively).

The temporal bisection task, one of the most widely used to study time perception, has helped to understand the psychophysics of time and the mechanisms of timing across different species. We extended the temporal bisection task to dogs. Five dogs were reinforced for choosing a yellow but not a blue stimulus after a 1-s tone, and for choosing a blue but not a yellow stimulus after a 4-s tone. After they learned this conditional discrimination, the dogs chose between the blue and yellow stimuli after tones with intermediate durations (1.4, 2.0, and 2.8 s). The results showed that the proportion of “Long” choices increased monotonically with stimulus duration. Moreover, the point of subjective equality was slightly below the geometric mean of the trained tone durations. These psychophysical results are consistent with those obtained with other nonhuman species, and suggest that common mechanisms underlie timing across different mammals and birds., This research was part of the scientific program of Instituto Nacional de Ciência e Tecnologia Sobre Comportamento, Cognição e Ensino, with support from the Brazilian National Research Council (CNPq, Grant 465686/2014-1) and the São Paulo Research Foundation (Grant 2014/50909-8). Camila Domeniconi had a postdoctoral fellowship from the Foundation for Research Support in the State of São Paulo (FAPESP, 2009/ 18479-5). She has a research productivity fellowship bythe National Council for Scientific and Technological Development (CNPq, 301623/2012-0). Armando Machado was supported by grant PTDC/MHC-PCN/ 3540/ 2012 from the Portuguese Foundation for Science and Technology., info:eu-repo/semantics/publishedVersion

The ability to identify stimuli that signal important events is fundamental for an organism to adapt to its environment. In the present paper, we investigated how more than one stimulus could be used jointly to learn a temporal discrimination task. Ten pigeons were exposed to a symbolic matching-to-sample procedure with three durations as samples (2, 6, and 18 s of keylight) and two colors as comparisons (red and green hues). A 30-s intertrial interval (ITI), illuminated with a houselight, separated the trials. Both the houselight and the sample keylight could control responding, so two tests were run to assess how these stimuli influenced choice. In the no-sample test, the keylight was not presented; in the dark-ITI test, the houselight was not illuminated. Results suggest that both houselight and keylight controlled choice, and with the exception of one animal, the more a pigeon relied on one of these stimuli, the less it appeared to rely on the other., The present work was conducted at the Psychology Research Centre, University of Minho, and was supported by the Portuguese Foundation for Science and Technology (FCT) and the Portuguese Ministry of Education and Science through national funds and when applicable co-financed by FEDER under the PT2020 Partnership Agreement (UID/PSI/01662/2013). This work was also supported by FCT Doctoral Grants to Carlos Pinto (SFRH/BD/78566/2011) and Ines Fortes (SFRH/BD/77061/2011), and a FCT Grant (PTDC/MHC-PCN/3540/2012) to Armando Machado., info:eu-repo/semantics/publishedVersion

Inspired by Spence's seminal work on transposition, we propose a synthetic approach to understanding the temporal control of operant behavior. The approach takes as primitives the temporal generalization gradients obtained in prototypical concurrent and retrospective timing tasks and then combines them to synthetize more complex temporal performances. The approach is instantiated by the learning-to-time (LeT) model. The article is divided into three parts. In the first part, we review the basic findings concerning the generalization gradients observed in fixed-interval schedules, the peak procedure, and the temporal generalization procedure and then describe how LeT explains them. In the second part, we use LeT to derive by gradient combination the typical performances observed in mixed fixed-interval schedules, the free-operant psychophysical procedure, the temporal bisection task, and the double temporal bisection task. We also show how the model plays the role of a useful null hypothesis to examine whether temporal control in the bisection task is relative or absolute. In the third part, we identify a set of issues that must be solved to advance our understanding of temporal control, including the shape of the generalization gradients outside the range of trained stimulus durations, the nature of temporal memories, the influence of context on temporal learning, whether temporal control can be inhibitory, and whether temporal control is also relational. These issues attest to the heuristic value of a Spencean approach to temporal control., The authors MPC, AM, and MV were supported by grants SFRH/BD/73875/2010, PTDC/MHC-PCN/3540/2012, and IF/01624/2013/CP1158/CT0012, respectively, from the Portuguese Foundation for Science and Technology. This study was conducted at the Psychology Research Centre, University of Minho, and partially supported by the Portuguese Foundation for Science and Technology and the Portuguese Ministry of Education and Science through national funds and when applicable co-financed by FEDER under the PT2020 Partnership Agreement (UID/PSI/01662/2013)., info:eu-repo/semantics/publishedVersion

Several studies have shown that, when offered a choice between an option followed by stimuli indicating whether or not reward is forthcoming and an option followed by noninformative stimuli, animals strongly prefer the former even when the latter is more profitable. Though this paradoxical preference appears to question the principles of optimal foraging theory, Vasconcelos, Monteiro, and Kacelnik (2015) proposed an optimality model that shows how such preference maximizes gains under certain conditions. In this paper, we tested the model's core assumption that a stimulus signaling the absence of food should not influence choice independently of its other properties, such as probability or duration. In 2 experiments, pigeons chose between 2 options: the "informative option" delivered food on 20% of the trials after a 10-s delay, signaled by a "good-news" stimulus, and delivered no food on the remaining 80% of the trials, signaled by a "bad-news" stimulus. The "noninformative option" delivered food after 10 s on 50% of the trials, regardless of the signal shown. In Experiment 1, the probability of the bad-news stimulus was manipulated from 0.80 to 1.00; in Experiment 2, the duration of the bad-news stimulus was increased every time pigeons preferred the informative option, reaching at least 200 s. Consistent with the model's predictions, pigeons clearly preferred the informative option even when the noninformative option delivered 9 (Experiment 1) and 35 (Experiment 2) times more food., This study was conducted at the Psychology Research Centre, University of Minho, Portugal, and was supported by the Portuguese Foundation for Science and Technology (FCT) and the Portuguese Ministry of Education and Science through national funds cofinanced by FEDER under the PT2020 Partnership Agreement (Grant UID/PSI/01662/2013). This work was also supported by FCT Grant PTDC/MHC-PCN/3540/2012 to Armando Machado. Ines Fortes and Marco Vasconcelos were supported by an FCT Doctoral Grant SFRH/BD/77061/2011 and an FCT Investigator Grant IF/01624/2013, respectively. We are grateful to Thomas Zentall and the members of the Animal Learning and Behavior Laboratory of University of Minho for their helpful comments on a prior version of this paper., info:eu-repo/semantics/publishedVersion

We examined whether temporal learning in a bisection task is absolute or relational. Eight pigeons learned to choose a red key after a t-seconds sample and a green key after a 3t-seconds sample. To determine whether they had learned a relative mapping (short -> Red, long -> Green) or an absolute mapping (t-seconds -> Red, 3t-seconds -> Green), the pigeons then learned a series of new discriminations in which either the relative or the absolute mapping was maintained. Results showed that the generalization gradient obtained at the end of a discrimination predicted the pattern of choices made during the first session of a new discrimination. Moreover, most acquisition curves and generalization gradients were consistent with the predictions of the learning-to-time model, a Spencean model that instantiates absolute learning with temporal generalization. In the bisection task, the basis of temporal discrimination seems to be absolute, not relational., The authors were supported by grants from the Portuguese Foundation for Science and Technology (FCT SFRH/BD/73875/2010 and PTDC/MHC-PCN/3540/2012). The study was conducted at the Psychology Research Centre of the University of Minho, and was partially supported by the Portuguese Foundation for Science and Technology and the Portuguese Ministry of Education and Science through national funds and cofinanced by FEDER under the PT2020 Partnership Agreement (UID/PSI/01662/2013). The authors thank Catarina Soares and Margarida Monteiro for helping with data collection, and the members of the Animal Learning and Behavior Lab for comments on a first version of the manuscript. Results reported here were presented at the 26th Meeting of the Spanish Society for Comparative Psychology, Braga, Portugal, and at the 2014 Annual Symposium of the Society for the Quantitative Analysis of Behavior, Chicago, Illinois., info:eu-repo/semantics/publishedVersion

We examined whether temporal context influences how animals produce a time interval. Six pigeons pecked one key to start an interval and then another key to end the interval. Reinforcement followed whenever the interval duration fell within a range of values signaled by the keylight colors. During Phase 1, keylight colors S1 and L1, intermixed across trials, signaled the ranges (0.5-1.5 s) and (1.5- 4.5 s), respectively. During Phase 2, colors S2 and L2 signaled the ranges (1.5-4.5 s) and (4.5-13.5 s), respectively. We asked whether the intervals produced in the presence of L1 and S2, stimuli signalling the same range, varied with their temporal context, short in Phase 1, long in Phase 2. The results showed that a) the intervals produced in the presence of the different keylight colors accorded with the main properties of temporal differentiation, including Weber’s law, b) the L1 intervals had slightly higher means than the S2 intervals, a weak contrast effect, c) the L1 intervals also had higher variability than the S2 intervals. An extension of the learning-to-time model to temporal differentiation tasks reproduced some of the major features of the data but left unanswered how context might change the model parameters., MPC, AM, and MV benefited from grants from the Portuguese Foundation for Science and Technology (FCT SFRH/BD/73875/2010, PTDC/MHC-PCN/3540/2012, and IF/01624/2013/CP1158/CT0012, respectively). This study was conducted at the Psychology Research Centre, University of Minho, and partially supported by the Portuguese Foundation for Science and Technology and the Portuguese Ministry of Education and Science through national funds and when applicable co-financed by FEDER under the PT2020 Partnership Agreement (UID/PSI/01662/2013). The authors thank Catarina Soares, Margarida Monteiro, Francisca Cunha, Janete Silva, Lénia Amaral, Pilar Niño and Sofia Ribeiro for help collecting data., info:eu-repo/semantics/publishedVersion

To understand how effort, defined by number of responses required to obtain a reward, affects reward value, five pigeons were exposed to a self-control task. They chose between two alternatives, 2s of access to food after a delay of 10s, and 6s of access to food after an adjusting delay. The adjusting delay increased or decreased depending on the pigeons' choices. The delay at which the two alternatives were equally chosen defined the indifference point. To determine whether requiring responses during the delay led to more impulsive (smaller-sooner rewards) or self-controlled (larger-later rewards) choices, we varied the number of required pecks during the 10-s delay to the 2-s reinforcer, and assessed how the requirement affected the indifference points. In the High Rate Phase, they had to peck at least 10 times during the delay; in the Low Rate Phase, they could peck at most 5 times during the delay. For four pigeons the indifference point increased with the response requirement; for one pigeon it decreased. The results suggest that, in general, reward value varies inversely with effort., This work was supported by the Portuguese Foundation for Science and Technology (FCT) Grant (PTDC/MHC-PCN/3540/2012) to Armando Machado and Marco Vasconcelos. Ines Fortes and Marco Vasconcelos were supported by an FCT Doctoral Grant (SFRH/BD/77061/2011) and an FCT Investigator Grant (IF/01624/2013), respectively. We are grateful to the members of the Animal Learning and Behavior Laboratory of University of Minho for their helpful comments on a prior version of this paper., info:eu-repo/semantics/publishedVersion

To contrast the classic version of the Scalar Expectancy Theory (SET) with the Behavioral Economic Model (BEM), we examined the effects of trial frequency on human temporal judgments. Mathematical analysis showed that, in a temporal bisection task, SET predicts that participants should show almost exclusive preference for the response associated with the most frequent duration, whereas BEM predicts that, even though participants will be biased, they will still display temporal control. Participants learned to emit one response (R[S]) after a 1.0-s stimulus and another (R[L]) after a 1.5-s stimulus. Then the effects of varying the frequencies of the 1.0-s and 1.5-s stimuli were assessed. Results were more consistent with BEM than with SET. Overall, this research illustrates how the impact of non-temporal factors on temporal discrimination may help us to contrast associative models such as BEM with cognitive models such as SET. Deciding between these two classes of models has important implications regarding the relations between associative learning and timing. This article is part of a Special Issue entitled: Associative and Temporal Learning., This research was supported by NIH grant MH033881. Jeremie Jozefowiez and Armando Machado acknowledge support from the Fundacao para a Ciencia e a Tecnologia as well as from the European project COST ISCH Action TD0904 "Time in Mental activity" (www.timely-cost.eu). We would like to thank Sean Gannon and Sarah Sterling for help running parts of the experiments, Mario Laborda, Bridget McConnell, Gonzalo Miguez, and James Witnauer for comments on an earlier version of this manuscript. Correspondence concerning this article should be addressed to Jeremie Jozefowiez, laboratoire URECA, Universite Lille Nord de France, Campus de Lille3, Domaine Universitaire du Pont de Bois, BP 60149, 58653 Villeneuve d'Ascq Cedex, France. jeremie.jozefowiez@univ-lille3fr.

Models of timing differ on two fundamental issues, the form of the representation and the content of learning. First, regarding the representation of time some models assume a linear encoding, others a logarithmic encoding. Second, regarding the content of learning cognitive models assume that the animal learns explicit representations of the intervals relevant to the task and that their behavior is based on a comparison of those representations, whereas associative models assume that the animal learns associations between its representations of time and responding, which then drive performance. In this paper, we show that some key empirical findings (timescale invariant psychometric curves, bisection point at the geometric mean of the trained durations in the bisection procedure, and location of the indifference point in the time-left procedure) seem to make these two issues interdependent. That is, cognitive models seem to entail a linear representation of time, and at least a certain class of associative models seem to entail a log representation of time. These interdependencies suggest new ways to compare and contrast timing models., Jeremie Jozefowiez and Armando Machado acknowledge support from the Fundacao para a Ciencia e a Tecnologia as well as from the European project COST ISCH Action TD0904 "Time in Mental activity" (www.timely-cost.eu)., info:eu-repo/semantics/publishedVersion

The experiment examined how pigeons differentiate response patterns along the dimension of number. Seven pigeons received food after pecking the left key at least N times and then switching to the right key (Mechner’s Fixed Consecutive Number schedule). Parameter N was set according to a percentile schedule, which is a form of automatic shaping. Our aim was twofold: on the empirical side to determine how run length on the left key would evolve under this shaping procedure and how it would change during a subsequent extinction phase; and on the theoretical side to compare the data with the predictions of a theoretical model of response differentiation. Results showed that during shaping, run length on the left key increased and then, for some pigeons, it stabilized, whereas for others pigeons it remained variable. Some pigeons ceased to respond when average run length reached a highvalue. There were substantial within-session trends in run length. In extinction, before the pigeons ceased to respond altogether, they emitted the same distribution of run lengths as during the last sessions of shaping with the exception, in some birds, of a large number of runs of length zero. These results are interpreted at the light of the theoretical model of numerosity differentiation.Keywords: Mathematical Model, Response Numerosity, Percentile Schedule, Shaping, Pigeon, O presente estudo analisa a diferenciação numérica de padrões de resposta. Em uma caixa de Skinner com duas teclas, sete pombos receberam comida após bicarem pelo menos N vezes na tecla esquerda e depois uma vez na tecla direita (programa “Fixed Consecutive Number” de Mechner). Em cada ensaio, o parâmetro N era ajustado por um programa de reforço percentil (uma forma de shaping automático). O estudo teve dois objetivos. Primeiro, determinar como é que varia o tamanho das corridas na tecla da esquerda durante o procedimento de modelagem (shaping) e durante uma fase de extinção que se seguiu. Segundo, comparar os dados obtidos com as previsões de um modelo teórico de diferenciação da resposta. Os resultados mostraram que, durante a modelagem, o tamanho das corridas na tecla esquerda aumentou e depois, para alguns pombos, estabilizou, enquanto para outros pombos permaneceu variável. Alguns pombos pararam de responder quando o tamanho médio da corrida atingiu valores elevados. Observaram-se ainda variações sistemáticas nos tamanhos das corridas no interior de cada sessão como, por exemplo, o aumento do tamanho da corrida ao longo da sessão. Durante a fase de extinção os pombos produziram distribuições de tamanhos de corrida semelhantes às distribuições produzidas durante as últimas sessões de modelagem com exceção, em alguns sujeitos, do elevado número de corridas de tamanho zero. Estes resultados são interpretados à luz do modelo teórico de diferenciação numérica das respostas. Palavras-chave: Modelo matemático, numerosidade, esquema percentil, modelagem, pombo

In a temporal double bisection task, animals learn two discriminations. In the presence of Red and Green keys, responses to Red are reinforced after 1-s samples and responses to Green are reinforced after 4-s samples; in the presence of Blue and Yellow keys, responses to Blue are reinforced after 4-s samples and responses to Yellow are reinforced after 16-s samples. Subsequently, given a choice between Green and Blue, the probability of choosing Green increases with the sample duration_the context effect. In the present study we asked whether this effect could be predicted from the stimulus generalization gradients induced by the two basic discriminations. Six pigeons learned to peck Green following 4-s samples (S+) but not following 1-s samples (S2) and to peck Red following 4-s samples (S+) but not following 16-s samples (S2). Temporal generalization gradients for Green and Red were then obtained. Finally, the pigeons were given a choice between Green and Red following sample durations ranging from 1 to 16 s. Results showed that a) the two generalization gradients had the minimum at the S2 duration, an intermediate value between the S2 and the S+ durations, and the maximum at the S+ as well as more extreme durations; b) on choice trials, preference for Green over Red increased with sample duration, the context effect; and c) the two generalization gradients predicted the average context effect well. The Learning-to-Time model accounts for the major trends in the data., The authors thank the students from the Animal Learning and Behavior laboratory of the University of Minho for their helpful comments on the paper. Ana Catarina Vieira de Castro was supported by a PhD fellowship and Armando Machado by a grant from the Portuguese Foundation for Science and Technology (FCT).

In the present study we extended errorless learning to a conditional temporal discrimination. Pigeons’ responses to a left–red key after a 2-s sample and to a right–green key after a 10-s sample were reinforced. There were two groups: One learned the discrimination through trial and error and the other through an errorless learning procedure. Then, both groups were presented with three types of tests. First, they were exposed to intermediate durations between 2 s and 10 s, and given a choice between both keys (stimulus generalization test). Second, a delay from 1 s to 16 s was included between the offset of the sample and the onset of the choice keys (delay test). Finally, pigeons learned a new discrimination in which the stimuli were switched (reversal test). Results showed that pigeons from the Errorless group made significantly fewer errors than those in the Trial-and-Error group. Both groups performed similarly during the stimulus generalization test and the reversal test, but results of the delay test suggested that, on long stimulus trials, responding in the errorless training group was less disrupted by delays., This research was presented in part at the 33rd Annual Convention of the Association of Behavioral Analysis (ABA) in San Diego, California. The authors were supported by the Portuguese Foundation for Science and Technology (FT). The authors thank Herbert S. Terrace for his valuable thoughts at the 31st Annual Meeting of the Society for the Quantitative Analyses of Behavior (SQAB) about this research.

The present experiment investigated whether pigeons can show associative symmetry on a two-alternative matching to-sample procedure The procedure consisted of a within subject sequence of training and testing with reinforcement and It provided (a) exemplars of symmetrical responding and (b) all prerequisite discriminations among test samples and comparisons After pigeons had learned two arbitrary matching tasks (A B and C D) they were given a reinforced symmetry test for half of the baseline relations (B1-A1 and D1-C1) To control for the effects of reinforcement during testing two novel nonsymmetrical responses were concurrently reinforced using the other baseline stimuli (D2-A2 and B2-C2) Pigeons matched at chance on both types of relations thus indicating no evidence for symmetry These symmetrical and nonsymmetrical relations were then directly trained in order to provide exemplars of symmetry and all prerequisite discriminations for a second test The symmetrical test relations were now B2-A2 and D2-C2 and the nonsymmetrical relations were D1-A1 and B1-C1 On this test 1 pigeon showed clear evidence of symmetry 2 pigeons showed weak evidence and 1 pigeon showed no evidence The previous training of all prerequisite discriminations among stimuli and the within subject control for testing with reinforcement seem to have set favorable conditions for the emergence of symmetry in nonhumans However the variability across subjects shows that methodological variables still remain to be controlled, This research was supported by Doctoral Grant (CNPq 142544/2005-1) and Doctoral Sandwich Grant (CAPES 4457-07 2) to Saulo M Velasco Doctoral Grant (FAPESP 60678-4/05) and Doctoral Sandwich Grant (CAPES 0103/08-0) to Edson M Huziwara Researcher Grant (CNPq 302640/2007-0) and Research Support (CNPq 471953/2004-0) to Gerson Y Tomanari Armando Machado was funded by the Portuguese Foundation for Science and Technology (FCT), info:eu-repo/semantics/publishedVersion

In the time-left procedure, a task used to study prospective timing, animals choose between two stimuli that signal different delays to reinforcement. Trials begin with one stimulus signaling C seconds to reinforcement and, at different moments since its onset, another stimulus, signaling S seconds to reinforcement, with C>S, is introduced. Optimal performance consists in choosing the stimulus signaling the shorter time to reinforcement. Animals have been found to perform in this optimal way. However, this procedure is complex and variables other than time may be responsible for the results. In two experiments with pigeons we sought to improve the time-left procedure to better isolate the effect of time in the animals' behavior. We attempted to control for two confounding variables, the asymmetry in the time markers from training to testing and the cost of switching between the two response alternatives. We conclude that in the time-left task pigeons seem indeed to regulate their behavior based on time because, with our improved procedure, they still chose the stimulus associated with the shorter time to food. However, our version of the procedure created new interpretative difficulties, strengthening the idea that the time-left procedure may be too complex to study timing., The authors would like to thank Luis Oliveira for his help in developing the present study and Jeremie Jozefowiez for comments on an earlier version of the manuscript. Work supported by the Portuguese Foundation for Science and Technology (FCT) grants SFRH/BD/43398/2008 and PTDC/PSI/65678/2006., info:eu-repo/semantics/publishedVersion

In the last decades, researchers have proposed a large number of theoretical models of timing. These models make different assumptions concerning how animals learn to time events and how such learning is represented in memory. However, few studies have examined these different assumptions either empirically or conceptually. For knowledge to accumulate, variation in theoretical models must be accompanied by selection of models and model ideas. To that end, we review two timing models, Scalar Expectancy Theory (SET), the dominant model in the Field, and the Learning-to-Time (LeT) model, one of the few models dealing explicitly with learning. In the first part of this article, we describe how each model works in prototypical concurrent and retrospective timing tasks, identify their structural similarities, and classify their differences concerning temporal learning and memory. In the Second part, we review a series of studies that examined these differences and conclude that both the memory structure postulated by SET and the state dynamics postulated by LeT are probably incorrect. In the third part, we propose a hybrid model that may improve on its parents. The hybrid model accounts for the typical findings in fixed-interval schedules, the peak procedure, mixed fixed interval schedules, simple and double temporal bisection, and temporal generalization tasks. In the fourth and last part, we identify seven challenges that any timing model trust meet., Fundação para a Ciência e a Tecnologia (FCT)

We examined if the representation of time intervals in a temporal discrimination task is based not only on their absolute but also on their relative durations. Six pigeons learned two temporal discriminations. In the first, red and green choices were correct following 2-s and 8-s samples, respectively. In the second, vertical and horizontal bar choices were correct following 4-s and 16-s samples, respectively. In a previous study [Zentall, T.R., Weaver, J.E., Clement, T.S., 2004. Pigeons group time intervals according to their relative duration. Psychon. Bull. Rev. 11, 113-117.]. tests with 4-s samples and red/green comparisons revealed a bias for red, whereas tests with 8-s samples with vertical/horizontal comparisons revealed a bias for horizontal. These results were interpreted in terms of relative encoding of sample durations. We attempted to replicate this finding but instead of testing with only 4-s or 8-s samples, we tested with several other sample durations to obtain a psychometric function. Results were inconsistent with the relative encoding hypothesis., Part of the work reported here was included in a Masters thesis submitted by the first author to the University of Minho, Portugal. Research supported by a grant from the Portuguese Foundation for Science and Technology (FCT) to the second author., info:eu-repo/semantics/publishedVersion

To test the assumptions of two models of timing, Scalar Expectancy Theory (SET) and Learning to Time (LeT), nine pigeons were exposed to two temporal discriminations, each signaled by a different cue. On half of the trials, pigeons learned to choose a red key after a 1.5-s horizontal bar and a green key after a 6-s horizontal bar; on the other half of the trials, they learned to choose a blue key after a 6-s vertical bar and a yellow key after a 24-s vertical bar. During subsequent test trials, they were exposed to the horizontal or vertical bar, for durations ranging from 1.5 to 24 s, and given a choice between novel key combinations: red vs. yellow, or green vs. blue. Results showed a strong effect of sample duration-as the test signal duration increased, preference for green over blue increased and preference for red over yellow decreased. The effect of sample cue was obtained only on the green-blue test trials. These effects are discussed in light of SET and LeT., The authors thank Francisco Silva for helpful comments. Research supported by a grant from the Portuguese Foundation for Science and Technology (FCT) to the second author., info:eu-repo/semantics/publishedVersion

We used a numerical bisection procedure to examine preschool children's sensitivity to the numerical attributes of stimuli. In Experiment I children performed two tasks. In the Cups Task they earned coins for choosing a green cup after two drumbeats and a blue cup after eight drumbeats. In the Gloves Task they earned coins for raising a red glove on their left hand after two drumbeats and a yellow glove on their right hand after eight drumbeats. Then in each task a psychometric function was obtained by presenting intermediate numerosities and recording the percentage of trials in which children chose the "many" option. In Experiment 2 children's performance in a '2 vs. 8' discrimination was compared with their performance in a "4 vs. 16" discrimination. Results showed that the individual psychometric functions were of two types, one in which the percentage of "many" choices increased gradually with stimulus numerosity and another in which it increased abruptly, in a step-like manner. Although the average point of subjective equality was close to the geometric mean of the anchor numerosities and the average functions for "2 vs. 8" and "4 vs. 16" superimposed when plotted on a common scale (the scalar property), the individual data were highly variable both across tasks (Cups and Gloves) and numerosity ranges (`2 vs. 8' and `4 vs. 16'). It is suggested that between-and within-subjects variability in the psychometric function is related to children's verbalizations about the sample stimulus., info:eu-repo/semantics/publishedVersion

Two experiments examined how pigeons differentiate response patterns along the dimension of number. In Experiment 1, 5 pigeons received food after pecking the left key at least N times and then switching to the right key (Mechner's Fixed Consecutive Number schedule). Parameter N varied across conditions from 4 to 32. Results showed that run length on the left key followed a normal distribution whose mean and standard deviation increased linearly with N; the coefficient of variation approached a constant value (the scalar property). In Experiment 2, 4 pigeons received food with probability p for pecking the left key exactly four times and then switching. If that did not happen, the pigeons still could receive food by returning to the left key and pecking it for a total of at least 16 times and then switching. Parameter p varied across conditions from 1.0 to .25. Results showed that when p= 1.0 or p=.5, pigeons learned two response numerosities within the same condition. When p=.25, each pigeon adapted to the schedule differently. Two of them emitted first runs well described by a mixture of two normal distributions, one with mean close to 4 and the other with mean close to 16 pecks. A mathematical model for the differentiation of response numerosity in Fixed Consecutive Number schedules is proposed., We thank Francisco Silva and Luı´s Oliveira for their comments. Research was supported by a grant from the Portuguese Foundation for Science and Technology (FCT;Pocti/Psi/44136/2002) to the first author., info:eu-repo/semantics/publishedVersion

Within the complex set of activities that comprise the scientific method, three clusters of activities can be recognized: experimentation, mathematization, and conceptual analysis. In psychology, the first two of these clusters are well-known and valued, but the third seems less known and valued. The authors show the value of these three clusters of scientific method activities in the works of the quintessential scientist Galileo Galilei. They then illustrate how conceptual analysis can be used in psychology to clarify the grammar and meaning of concepts, expose conceptual problems in models, reveal unacknowledged assumptions and steps in arguments, and evaluate the consistency of theoretical accounts. The article concludes with a discussion of three criticisms of conceptual analysis., Armando Machado was funded by a grant from the Portuguese Foundation for Science and Technology. We thank Susan Goldstein for sharing her expertise about construct validity, info:eu-repo/semantics/publishedVersion

Pigeons were placed in a long chamber equipped with one key and feeder at each end side and one key and houselight at the middle. To obtain food the birds had to choose one side key after a short signal and the other side key after a long signal. The signals consisted of the illumination of the center key and the houselight and were initiated by a peck at the center key. The chamber had sensitive floor panels that enabled us to measure the location of the bird during the signals. In Experiment 1, after the birds learned the discrimination we reversed the assignment of keys to signals. In Experiment 2, we examined performance on two pairs of discriminations holding the same ratio. In Experiment 3, after the pigeons learned to discriminate two signals, we changed the duration of the long signal. The results showed that (a) the birds' motion during the signal was highly stereotypical, i.e. the birds moved to the short side, waited a few seconds, and then departed to, and stayed on the long side; (b) this motion pattern predicted the results of generalization tests with novel durations; (c) the mean of the times of departure from the short side approached its steady state values quicker than the standard deviation and consequently superposition of behavioral measures became stronger with training; (d) only the duration of the short signal influenced significantly the moment the birds departed from the short side: finally (e) the times of arrival at and departure from the short side were positively correlated, but the times of arrival and residence at the short side were negatively correlated., info:eu-repo/semantics/publishedVersion

We reviewed Daniel Povinelli's book, Folk physics for apes: The chimpanzee's theory of how the world works. After a summary of the book's contents, we analyzed two sets of experiments on chimpanzees' folk psychology: one that explored whether chimpanzees understand that others see (i.e., that apes have internal visual experiences) and another that examined whether chimpanzees can distinguish intended from unintended actions. The conceptual scaffolding on which these studies were conceived was sufficiently faulty that their outcomes were virtually assured a priori. We then analyzed two sets of experiments on chimpanzees' folk physics, reinforcing our view that conceptual confusion guaranteed that certain key predictions about the outcome of these studies could not be supported. A unifying reason for this conceptual confusion is that the author devalues understanding that results from programmatic conditioning. We closed the review by relating Povinelli's findings and conclusions to behavior analysis and by explaining why behavior analysts should read this book.