Further tests of the Scalar Expectancy Theory (SET) and the Learning-to-Time (LeT) model in a temporal bisection task

doi:10.1016/j.beproc.2006.03.001

Behavioural Processes

Volume 72, Issue 3, 1 June 2006, Pages 195-206

https://doi.org/10.1016/j.beproc.2006.03.001 Get rights and content

Abstract

To contrast two models of timing, Scalar Expectancy Theory (SET) and Learning to Time (LeT), pigeons were exposed to a double temporal bisection procedure. On half of the trials, they learned to choose a red key after a 1 s signal and a green key after a 4 s signal; on the other half of the trials, they learned to choose a blue key after a 4-s signal and a yellow key after a 16-s signal. This was Phase A of an ABA design. On Phase B, the pigeons were divided into two groups and exposed to a new bisection task in which the signals ranged from 1 to 16 s and the choice keys were blue and green. One group was reinforced for choosing blue after 1-s signals and green after 16-s signals and the other group was reinforced for the opposite mapping (green after 1-s signals and blue after 16-s signals). Whereas SET predicted no differences between the groups, LeT predicted that the former group would learn the new discrimination faster than the latter group. The results were consistent with LeT. Finally, the pigeons returned to Phase A. Only LeT made specific predictions regarding the reacquisition of the four temporal discriminations. These predictions were only partly consistent with the results.

Section snippets

Subjects

Ten naïve pigeons (Columbia livia) maintained at 80% of their free-feeding body weight participated in the experiment. The pigeons had continued access to water and grit in their home cages. The pigeon colony was under a 12:12 h light–dark cycle.

Apparatus

Two standard experimental chambers from Med Associates© were used. The front panel of each chamber contained three keys, 2 cm in diameter. The keys were centered on the wall, 22 cm above the floor, and 8 cm apart, center to center. They could be illuminated

Phase A

All pigeons learned the two basic discriminations. During the last five sessions of Phase A, overall proportion correct was consistently high both across birds (average = 0.93) and signal durations (range: 0.85–0.99). These results reproduce the earlier findings of Machado and Keen (1999) and Machado and Pata (2005).

Phase B

Fig. 5 shows the average results from this phase for the first, second, and 10th (last) sessions. Consider the top panel, which illustrates the data from Group Consistent: as the

Discussion

The present study used a variation of the temporal bisection procedure to contrast the predictions of two models of timing, SET and LeT. During Phase A of an ABA design, 10 pigeons learned 2 temporal discriminations, to choose a red key after a 1-s signal and a green key after a 4-s signal, and to choose a blue key after a 4-s signal and a yellow key after a 16-s signal. During Phase B, the pigeons were exposed to signals ranging from 1 to 16 s and at the end of the signal they chose between the

Acknowledgements

The authors thank students Paulo Pata and Paula Magalhães for their help in running the experiment. Research supported by a grant from the Portuguese Foundation for Science and Technology to the first author.

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The context effect as interaction of temporal generalization gradients: Testing the fundamental assumptions of the Learning-to-Time model
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Citation Excerpt :
Finally, on test trials, the pigeon is exposed to samples of different durations and to a new key combination, Green and Blue, the keys previously reinforced following the common 4-s sample. The critical finding is that preference for Green over Blue increases as the sample duration ranges from 1 s to 16 s. Machado and Keen (1999); see also Arantes, 2008; Arantes and Machado, 2008; Machado and Arantes, 2006; Machado and Pata, 2005; Oliveira and Machado, 2008, 2009; Vieira de Castro and Machado, 2012) referred to this finding as a context effect because it suggests that the sample contexts in which the Green and Blue keys were trained, Green with a shorter sample, and Blue with a longer sample, affected how the preference for each key varied with the sample duration. The Learning-to-Time model (LeT; Machado, 1997; Machado et al., 2009), a behavioral model developed on the basis of earlier work by Killeen and Fetterman (1988), can account for the context effect.
To test the Learning-to-Time model, six pigeons learned two temporal bisection tasks. In one task they learned to choose a Red key over a Green key following 2-s samples and the Green key over the Red key following 6-s samples; in another task, they learned to choose a Blue key over a Yellow key following 6-s samples and the Yellow key over the Blue key following 18-s samples. After each task was learned, temporal generalization gradients were obtained with samples ranging from 0.7 s to 51.4 s. Finally, preference for Green over Blue – the keys associated with the common 6-s duration, was determined as a function of sample duration. Two issues were examined, whether the preference for Green over Blue increased with sample duration, a transposition-like effect reported before, and whether the preference for Green over Blue could be predicted from the generalization gradients for Green and Blue previously obtained. Results showed that preference for Green over Blue increased with sample duration and that the general shape of the function could be predicted from the generalization gradients. The Learning-to-Time model accounted well for the major trends in the data.
This article is part of a Special Issue entitled: SQAB 2012.
Context effect in a temporal bisection task with the choice keys available during the sample
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In a symbolic matching to sample task, six pigeons learned to associate different sample durations with different comparison stimuli. On “Short” trials, choice of Red and Green keylight comparisons were reinforced following 3-s and 9-s samples, respectively; on “Long” trials, Blue and Yellow keylight comparisons were reinforced following 9-s and 27-s samples, respectively. In contrast with previous studies, the comparison keys were available during the samples. After the temporal discriminations were learned, new pairs of comparison keys were presented and the preference for each was assessed during 27-s samples. One pair in particular, Green and Blue, was critical because it tested the predictions of two timing models, Scalar Expectancy Theory (SET) and the Learning-to-Time (LeT) model. The results showed that preference for Green increased during the sample, a result consistent with LeT but not with SET. Other test results, however, were predicted by neither model.
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The present research tested the generality of the “context effect” previously reported in experiments using temporal double bisection tasks [e.g., Arantes, J., Machado, A. Context effects in a temporal discrimination task: Further tests of the Scalar Expectancy Theory and Learning-to-Time models. J. Exp. Anal. Behav., in press]. Pigeons learned two temporal discriminations in which all the stimuli appear successively: 1 s (red) vs. 4 s (green) and 4 s (blue) vs. 16 s (yellow). Then, two tests were conducted to compare predictions of two timing models, Scalar Expectancy Theory (SET) and the Learning-to-Time (LeT) model. In one test, two psychometric functions were obtained by presenting pigeons with intermediate signal durations (1–4 s and 4–16 s). Results were mixed. In the critical test, pigeons were exposed to signals ranging from 1 to 16 s and followed by the green or the blue key. Whereas SET predicted that the relative response rate to each of these keys should be independent of the signal duration, LeT predicted that the relative response rate to the green key (compared with the blue key) should increase with the signal duration. Results were consistent with LeT's predictions, showing that the context effect is obtained even when subjects do not need to make a choice between two keys presented simultaneously.
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The switch time offers a measure of temporal discrimination that is not dependent on arbitrary probe durations, as in the more popular bisection procedure (e.g., Church and Deluty, 1977). This conditional switch procedure bears a strong resemblance to the method pioneered by Platt and Davis (1983) for pigeons that has recently been extended to mice (Balci et al., in press), and the double bisection procedure that allows testing of multiple pairs of intervals simultaneously (Machado and Arantes, 2006; Machado and Keen, 1999; Machado and Pata, 2005). The conditional switch approach combines the best of these two innovations, allowing for the examination of switching behavior during the intervals as well as cross-pair comparisons in the same session.
A conditional temporal discrimination procedure was used to test the scope and generality of the principle of timescale invariance (TSI). Rats were trained to make different temporal discriminations following four different auditory stimuli. After shorter stimuli, rats were reinforced for pressing the left lever, and after longer stimuli, rats were reinforced for pressing the right lever. The four auditory stimuli (a pure tone, pulsed tone, click, and white noise) were each presented for different pairs of durations (ranging from 2 vs. 8 s to 32 vs. 128 s) within a single session, but the ratio between the shorter and longer duration was maintained constant at 1:4. With the shortest pair of durations (2 vs. 8 s), rats showed a clear violation of TSI in both overall and relative response rates. Rats started responding later and persisted relatively longer on the left lever when the shorter duration was only 2 s. We interpret these results with regards to a framing hypothesis, whereby TSI does not apply to relatively short durations when animals are simultaneously trained with wide ranges of intervals.
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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.
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Operant behavior is behavior guided by its consequences. Conditioning operant behavior requires making a biologically important event, or a stimulus signaling such an event, depend on the occurrence of a target operant response. If this arrangement leads to an increase in the probability of the target response, the contingent event is termed a reinforcer and the associated process reinforcement. In this chapter, we review the conditions under which reinforcement takes place, that is, how an animal is able to detect that a reinforcer is delivered as the consequence of the emission of a behavior (operant learning). We look at how behavior is modulated by its consequences in situations in which reinforcement occurs at a fixed time after a specific event (interval timing) and situations in which the animal has the choice between several response alternatives, each reinforced according to a different rule (operant choice). Finally, we review theories that explain why some events have reinforcing properties (reinforcement theory).

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Further tests of the Scalar Expectancy Theory (SET) and the Learning-to-Time (LeT) model in a temporal bisection task

Abstract

Section snippets

Subjects

Apparatus

Phase A

Phase B

Discussion

Acknowledgements

Learn. Motiv.

J. Math. Psychol.

Learn. Motiv.

Behav. Process.

Behav. Process.

Reinforcement schedules and the psychophysical judgments: a study of some temporal properties of behavior

Bisection of temporal intervals

J. Exp. Psychol.: Anim. Behav. Process.

Watching the clock

Behav. Process.

The Organization of Learning

The Symbolic Foundations of Conditioned Behavior