1st International Workshop on the Multidisciplinary Aspects of Time Perception
Jeremie Jozefowiez & Armando Machado
Universidade do Minho
Portugal
1st TIMELY Workshop
Athens, October 8th 2010
Studies of timing using operant conditioning
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
Various models have been developed within this framework:
SET, BET, LeT, MTS, packet theory, BEM,…
All of these models have three main components:
1.A short-term memory representation of the time elapsed since the time-marker
2.A long-term memory representation of the time of reinforcement
3.A
3 A decision rule explaining how the STM and the LTM representation determine
behavior
This p
presentation will deal mainly
y with the decision rule
Two types of decision rules: “COGNITIVE” and “ASSOCIATIVE”
Cognitive decision rules
The STM and the LTM representation are two numbers
Behavior is determined by a comparison between those two numbers
Ex: Scalar Expectancy Theory (SET.
(SET Gibbon,
Gibbon Church,
Church & Meck,
Meck 1984)
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
Associative decision rules
The time-marker triggers a series of time-dependent state
Association between a state and a response increases proportionally to its level
of activation in case of reinforcement, decreases otherwise
Ex: Learning
Learning-to-time
to time model (LeT.
(LeT Machado,
Machado 1997)
Cognitive and associative models differ in their prediction relative to two general
classes of phenomena
1.
Reinforcement should intrinsically affect timing performance according to
associative models
2.
The long-term memory representation of time is context-specific
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
Reinforcement parameters should affect timing
Ex: Temporal discrimination (bisection) task
1 s -> emit R1
4 s -> emit R2
x
R1
x
R2
R1
Case 1: R1 and R2 are equally
reinforced
R2
Case 2: R1 is more reinforced than
R2
Free-operant psychophysical procedure (FOPP)
p1
p2
50 s
p1=p2
p1<p2
p1>p2
p
p
Bizo & White (1995). J.Exp.Anal.Behav, 64, 225
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
LeT (Machado & Guilhardi, 2000)
BEM (Jozefowiez et al., 2009)
A cognitive rule could account for these data through the manipulation of a response
bias parameter
Wearden & Grindrod (2003)
p1
p2
p3
p4
60 s
p2=p3
p2=p3
Machado & Guilhardi (2000). J.Exp.Anal.Behav, 74, 25
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
Cognitive and associative models differ in their prediction relative to two general
classes of phenomena
1.
Reinforcement should intrinsically affect timing performance according to
associative models
2.
The long-term memory representation of time is context-specific
Task 1
Task 2
1s
R1
4s
R3
4s
R2
16 s
R4
Probability to pick R2
Test
R2
1-16 s
R3
Machado & Pata (2005). Learn. Behav. 33, 111
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
All of these models have three main components:
1.A short-term memory representation of the time elapsed since the time-marker
2.A long-term memory representation of the time of reinforcement
3.A decision rule explaining how the STM and the LTM representation determine
behavior
Weber’s law is respected only for some combinations of a STM representation scheme
and
d off a decision
d i i rule
l
“Scalar” encoding
The STM representation of an interval t
Is a random variable drawn from a
Gaussian distribution with mean at and
Standard deviation kat
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
A “scalar” encoding scheme does not seem to work well when combined with an
associative rule
Ex: Simulations of the bisection procedure by BEM (Jozefowiez et al., 2010)
Logarithmic encoding
“Scalar” encoding
Other arguments
Machado et al. (2010) compared the original version of Let to a “hybrid” version using the same associative rule and learning
Algorithms but a SET-like scalar representation
The model did not fair as well as the original LeT version, notably in the bisection procedure
Both Roberts (2006) and Yi (2009) concluded that their data from a temporal discrimination task were better explained by
an associative model using a logarithmic representation than by a similar model using a scalar SET-like representation
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
The time-left procedure
Time-left
Standard
F(S) = F(C) – F(T)
Logarithmic
T = C/S
Linear
T=C-S
Gibbon & Church (1981). J.Exp.Psych.Anim.Behav.Proc., 11, 113-117
Jozefowiez et al. (2009). Psychological Review, 116, 519-539
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1st International Workshop on the Multidisciplinary Aspects of Time Perception
Conclusion
Time perception in operant conditioning is affected by reinforcement
Time perception in operant conditioning is context-dependent
Those facts are more easily assimilated by models using associative decision
rules than models using cognitive decision rules
Determining which decision mechanism is more accurate might indirectly have
Implications concerning the nature of subjective time
Further research should:
1. Expand the cognitive models so they can deal efficiently with those effects
2. Investigate further the effect of reinforcement on time perception
3. Investigate further the context-dependency of time perception
4. Clarify the conditions under which Weber’s law is respected in a model using
an associative decision rule
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