SQAB – 31st Annual Meeting Chicago, May 22 – 24, 2008 Abstract: In double temporal bisection procedures, pigeons learn to discriminate two pairs of stimulus durations (eg: 2” vs 8”; 4” vs 16”) by pecking at different comparison stimuli. Tests at intermediate durations corresponding to a stimulus in the competing discrimination (eg: 4” or 8”) have shown response bias for the relative duration associated to that stimulus – short or long (Zentall et al., 2004). We obtained indifference on the same test durations and argue that both results are dynamic outcomes of basic contingencies of reinforcement. Following Davison and Nevin (1999), we describe the double bisection task as a 4-stimulus, 4-Response conditional discrimination procedure, assume generalization across stimuli and responses and predict choice based on the relative value of the alternatives. We show how this model can generate different psychometric functions, fit the model to our data, and test novel predictions from the estimated parameters.

1. The Contingencies of Time Discrimination:
a signal-detection analysis
José Bentes and Susana Maia
University of Minho, Portugal
Davison-Nevin
(1999)
S1
S2
B1 B2
B11. R11
B22. R22
B12
B21
48 57
72 48
45 0
0 40
30 0
0 26.4
22.7 27.3
30 20
45.5 10.1
11.4 40
45.5 10.1
11.4 40
45.5 10.1
11.4 40
Events on a conditional discrimination
dbr
B1 B2
12
12
22
11
br
sb d
d
R
R 
12
22
12
11
sb
br d
R
d
R

12
22
12
11
br
sb d
R
d
R

12
12
11
22
br
sb d
d
R
R 
S1
S2
dsb
Generalized reinforcement value
B11 B12
B21 B22
S1 
Response allocation (choice)
V(R11) V(R12)
V(R12) V(R21)
Relative pay-off
V(R11) = p R11 * (B11/B11+B12)
Response
Matrix
Generalized Value
pRf. = .66
pRf. = .5 (Rnd)
pRf. = 1
12
22
12
11
)
(
)
(
sb
br
d
R
V
d
R
V

12
12
22
11
)
(
)
(
br
sb
d
d
R
V
R
V 
12
22
12
11
)
(
)
(
br
sb
d
R
V
d
R
V

12
12
11
22
)
(
)
(
br
sb
d
d
R
V
R
V 
Training 1 Training 2 Testing
R11
R22
R33
R44
R11
R22
R33
R44
22
12
11
12
22
11
12
12
12
12
11
12
12
22
11
12
11
22 R
d
R
d
R
R
d
d
c
d
R
d
R
d
d
R
R
c
B
B
br
sb
br
sb
sb
br
br
sb






Partial reinforcement effects on Value
Zentall
et al.
(2004)
Machado
& Maia
(2008)
2 sec
16 sec
4 sec
8 sec
Double temporal bi-section
PSE
PSE
4 or 16 sec
2 or 8 sec 4 sec 8 sec
4 or 16 sec 4 or 16 sec
2 or 8 sec
2 or 8 sec
Training 1 Training 2 Testing
5.7, 8, 11.3 sec
?
2.8, 4, 5.7 sec
?
Ext.
Rnd
Rf.
?
?
2 or 8 sec
4”
16”
2”
S3
S4
S1
S2 8”
B1 B2 B3 B4
B1 B2
B3 B4
4”
16”
2”
S3
S4
S1
S2 8”
4”
S3
16”
S4
2”
S1
S2 8”
5.7”
2.8”
11.3”
B3 B4
B1 B2
0
0.5
1
2 2.8 4 5.7 8
Psychometric functions – parametric effects
Choose
“Short”
0
0.5
1
2 2.8 4 5.7 8
0
0.5
1
2 2.8 4 5.7 8
0
0.5
1
2 2.8 4 5.7 8
0
0.5
1
2 2.8 4 5.7 8
0
0.5
1
2 2.8 4 5.7 8
Dbr12= 60
Dbr23= 60
Dsb12= 2
Dsb23= 3
Dbr12= 5
Dbr23= 60
Dsb12= 2
Dsb23= 2
Dbr= 4 *
Dsb= 3
* Generalization across all responses
R11= 100
R22= 50
R33= 100
R44= 100
R11= 100
R22= 50
R33= 50
R44= 100
Stimulus Duration (sec.)
R11= 100
R22= 50
R33= 100
R44= 50
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2 2,8 4 5,7 8
Proporção
"Curto"
P819
2vs8
4vs16
Tests of novel response combinations
Stimulus Duration (sec.)
Choose
“Short”
0
0.5
1
2 4 8 16
P818
0
0.5
1
2 2.8 4 5.7 8 11.3 16
Model
100.4 26.8 33.6 11.7
101.0 35.1 67.1 14.5
51.0 51.0 100.3 18.4
35.1 101.1 67.2 23.4
26.8 100.4 34.0 34.0
21.8 100.8 23.4 67.2
17.6 50.5 18.4 100.3
Choose
“Short”
Stimulus Duration (sec.)