Kognitive Architekturen

1
Introduction to ACT-R Tutorial 21st Annual
Conference Cognitive Science Society
ACT-R Home Page http//act.psy.cmu.
edu
John R. Anderson Christian Lebiere Psychology
Department Carnegie Mellon University Pittsburgh,
PA 15213 ja_at_cmu.edu cl_at_cmu.edu
Dieter Wallach Institut fur Psychologie
Universitaet Basel Bernoullistr. 16 CH-4056
Basel wallachd_at_ubaclu.unibas.ch
2
Tutorial Overview
1. Introduction 2. Symbolic ACT-R Declarative P
rocedural Learning 3. Subsymbolic Performance
in ACT-R Activation (Declarative) Utility
(Procedural) 4. Subsymbolic Learning in
ACT-R Activation (Declarative) Utility
(Procedural) 5. ACT-R/PM Note For detailed
(40-100 hrs) tutorial, visit ACT-R Education
link. For software visit ACT-R
Software link. For models visit
Published ACT-R Models link.
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Unified Theories of Cognition
ACT-R exemplifies what Newell meant when he spoke
of a unified theory of cognition i.e., a single
system within which we can understand the wide
range of cognition. Arguments against Unified
Theories 1. Modularity behavioral and neural
evidence. 2. Need for specialization - Jack of
all trades, master of none. Argument for Unified
Theories 1. System Organization - We need to
understand how the overall mental system works
in order to have any real understanding of the
mind or any of its more specific functions.
2. Mental plasticity ability to acquire new
competences.
4
Newells Constraints on a Human Cognitive
Architecture (Newell, Physical Symbol Systems,
1980)
1. Behave as an (almost) arbitrary function
of the environment (universality) 2.
Operate in real time 3. Exhibit rational,
i.e., effective adaptive behavior 4. Use
vast amounts of knowledge about the environment
5. Behave robustly in the face of error, the
unexpected, and the unknown 6. Use symbols
(and abstractions) 7. Use (natural)
language - 8. Exhibit self-awareness and a
sense of self 9. Learn from its
environment 10. Acquire capabilities through
development - 11. Arise through evolution 12.
Be realizable within the brain
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The Missing Constraint Making Accurate
Predictions about Behavioral Phenomena.
ACT-R is explicitly driven to provide models for
behavioral phenomena. The tasks to which ACT-R
has been applied include 1. Visual search
including menu search 2. Subitizing 3. Dual
tasking including PRP 4. Similarity
judgements 5. Category learning 6. List
learning experiments 7. Paired-associate
learning 8. The fan effect 9. Individual
differences in working memory 10. Cognitive
arithmetic 11. Implicit learning (e.g. sequence
learning) 12. Probability matching experiments
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13. Hierarchical problem solving tasks including
Tower of Hanoi 14. Strategy selection
including Building Sticks Task 15. Analogical
problem solving 16. Dynamic problem solving tasks
including military command and
control 17. Learning of mathematical skills
including interacting with ITSs 18.
Development of expertise 19. Scientific
experimentation 20. Game playing 21. Metaphor
comprehension 22. Learning of syntactic cues 23.
Syntactic complexity effects and ambiguity
effects 24. Dyad Communication
A priori ACT-R models can be built for new
domains taking knowledge representations and
parameterizations from existing domains. These
deliver parameter-free predictions for phenomena
like time to solve an equation.
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History of the ACT-framework
Predecessor HAM (Anderson Bower
1973) Theory versions ACT-E (Anderson,
1976) ACT (Anderson, 1978) ACT-R (Ander
son, 1993) ACT-R 4.0 (Anderson Lebiere,
1998) Implementations GRAPES (Sauers
Farrell, 1982) PUPS (Anderson Thompson,
1989) ACT-R 2.0 (Lebiere Kushmerick,
1993) ACT-R 3.0 ACT-R 4.0 (Lebiere,
1998) ACT-R/PM (Byrne, 1998)
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ACT-R Information Flow
ACT-R Information Flow
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ACT-R Knowledge Representation
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ACT-R Assumption Space
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Chunks Example
(
)
CHUNK-TYPE
NAME
SLOT1
SLOT2
SLOTN
(
(
NEWCHUNK
FACT34
NAME
ADDITION-FACT
isa
isa
SLOT1
Filler1
ADDEND1
THREE
SLOT2
Filler2
ADDEND2
FOUR
)
)
SLOTN
FillerN
SUM
SEVEN
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Chunks Example
(CLEAR-ALL) (CHUNK-TYPE addition-fact addend1
addend2 sum) (CHUNK-TYPE integer value) (ADD-DM
(fact34 isa addition-fact addend1 three
addend2 four sum seven) (three isa
integer value 3) (four isa integer
value 4) (seven isa integer value 7)
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Chunks Example
ADDITION-FACT
3
7
VALUE
isa
VALUE
ADDEND1
SUM
FACT34
THREE
SEVEN
ADDEND2
4
isa
isa
FOUR
VALUE
isa
INTEGER
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Chunks Exercise I
Fact
The cat sits on the mat.
proposition
isa
(Add-DM (fact007 isa proposition agent
cat007 action sits_on object mat) )
cat007
fact007
mat
agent
object
action
sits_on
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Chunks Exercise II
Fact
The black cat with 5 legs sits on the mat.
proposition
cat
isa
isa
legs
cat007
5
mat
fact007
agent
object
color
action
black
sits_on
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Chunks Exercise III
(Chunk-Type proposition agent action
object) (Chunk-Type prof money-status
age) (Chunk-Type house kind price
status) (Add-DM (fact008 isa
proposition agent prof08 action buys object
house1001 ) (prof08 isa
prof money-status rich age young )
(obj1001 isa house kind city-house price
expensive status beautiful ) )
Fact
The rich young professor buys a beautiful and
expensive city house.
Chunk
proposition
house
expensive
prof
isa
price
isa
isa
agent
object
fact008
rich
obj1001
prof08
money- status
kind
status
action
age
beautiful
city-house
buys
young
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Productions
set of productions, organized through reference
to goals
procedural memory
modularity abstraction goal factoring
conditional asymmetry
productions
Structure of productions
(
p
name
ltGoal patterngt ltChunk retrieval gt
condition part
delimiter
gt
ltGoal Transformationgt ltExternal actiongt
action part
)
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Psychological reality of productions
Taken from Anderson, J.R. (1993). Rules of the
mind. Hillsdale, NJ LEA.
19
Error rates Data Model
Taken from Anderson, J.R. Lebiere, C. (1998).
The atomic components of thought. Hillsdale, NJ
LEA.
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Add-numbers

• (p add-numbers
• goalgt
• isa add-column
• num1 add1
• num2 add2
• result nil
• factgt
• isa addition-fact
• addend1 add1
• addend2 add2
• sum sum
• gt
• goalgt
• result sum
• )

production name
goal pattern
head/slot separator
gt
fact

chunk retrieval
variable prefix
action description
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3 4
Add-numbers
?
the goal is to add numbers in a column
and add1 is the first number and add2 is
the second number and you remember an
addition fact that add1 plus add2
equals sum
IF
Then
note in the goal that the result is sum
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Pattern matching
left-hand side
goalgt isa find-sum addend2 num2 sum
sum
negation
factgt isa add-fact addend1 zero addend2
num2 sum sum

addend1
goal
(goal1 isa find-sum addend1 nil addend2
two sum four )
declarative memory
(fact23 isa add-fact addend1 two addend2
three sum five)
(fact31 isa add-fact addend1 three
addend2 one sum four)
(fact04 isa add-fact addend1 zero
addend2 four sum four)
(fact22 isa add-fact addend1 two addend2
two sum four)
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Counting Example
Web Address ACT-R Home Page Published
ACT-R Models Counting Example
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Goal Stack
G3
G4
G2
G1
G2
G1
G1
G1
!push! G2
!focus-on! G4
!pop!
Initial state
stack-manipulating actions
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Tower of Hanoi Demo
Start-Tower IF the goal is to move a
pyramid of size n to peg x and size n
is greater than 1 THEN set a subgoal to move
disk n to peg x and change the goal to
move a pyramid of size n-1 to peg x
Final-Move IF the goal is to move a
pyramid of size 1 to peg x THEN move disk 1 to
peg x and pop the goal Subgoal-Block
er IF the goal is to move disk of size n
to peg x and y is the other peg
and m is the largest blocking disk THEN
post the goal of moving disk n to x in the
interface and set a subgoal to move
disk m to y Move IF the goal is move
disk of size n to peg x and there
are no blocking disks THEN move disk n to peg x
and pop the goal
Web Address ACT-R Home Page
Published ACT-R Models Atomic
Components of Thoughts Chapter
2 Model for Ruiz
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Tower of Hanoi Data Models
Taken from Anderson, J.R. Lebiere, C. (1998).
The atomic components of thought. Hillsdale, NJ
LEA.
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Subsymbolic level
Summary

• Computations on the subsymbolic level are
  responsible for
• which production ACT-R attempts to fire
• how to instantiate the production
• how long the latency of firing a production is
• which errors are observed
• As with the symbolic level, the subsymbolic level
  is not a static level, but is changing in the
  light of experience to allow the system to adapt
  to the statistical structure of the environment.

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Chunks Activation
A
-
F
D
D
I
T
I
O
N
A
C
T
i
s
a
(p add-numbers goalgt isa add-column
num1 add1 num2 add2
result nil
addend1
sum
F
3

4
A
C
T
T
S
H
R
E
E
E
V
E
N
Sji
Sji
B
i
W
j
Sji
a
d
d
e
n
d
2
factgt isa addition-fact addend1
add1 addend2 add2 sum sum
F
O
U
R
W
j
(goal1 isa add-column num1 Three num2
Four result nil )
AiBiSWjSji
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Chunk Activation
Context activation
)
(
base activation
associative strength


source activation
activation

Ai Bi ?Wj Sji
j
Activation makes chunks available to the degree
that past experiences indicate that they will be
useful at the particular moment
Base-level general past usefulness
Context relevance in the current context
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Base-level Activation
)
(
associative strength
source activation


base activation
activation

Ai Bi ?Wj
Sji
The base level activation Bi of chunk Ci reflects
a context-independent estimation of how likely Ci
is to match a production, i.e. Bi is an estimate
of the log odds that Ci will be used. Two
factors determine Bi frequency of using
Ci recency with which Ci was used
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Base-Level Activation Noise
Basel-level activation fluctuates and decays with
time
B(t) ? - d ln(t) ?1 ?2
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Source Activation
)
(
base activation
associative strength
source activation


activation

Ai Bi ? Wj
Sji
j
The source activations Wj reflect the amount of
attention given to elements, i.e. fillers, of
the current goal. ACT-R assumes a fixed capacity
for goal elements, and that each element has an
equal amount (W ? Wi 1).
(1) constant capacity for source activations (2)
equally divided among the n goal elements
constant/n (3) W reflects an individual
difference parameter
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Associative strength
)
(
base activation
associative strength
source activation


activation

Ai Bi ? Wj
Sji
The association strength Sji between chunks Cj
and Ci is a measure of how often Ci was needed
(retrieved) when Cj was element of the goal, i.e.
Sji estimates the log likelihood ratio of Cj
being a source of activation if Ci was retrieved.
( )
Sji ln
S - ln(P(NiCj))
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Retrieval time
Chunks i to instantiate production p are
retrieved sequentially
?
Retrieval-timep
Timeip
i
Time to retrieve a chunk as function of match
score Mip and strength of matching production Sp
Retrieval time is an exponential function of the
sum of match score of the chunk and the
production strength
35
Retrieval time
36
Fan effect

Lawyer
Park


In

Church
Fireman
Bank
Doctor
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Fan Effect Demo
Retrieve-by-Person If the goal is to retrieve a
sentence involving a person and a location and
there is a proposition about that person in some
location Then store that person and location as
the retrieved pair. Retrieve-by-Location If the
goal is to retrieve a sentence involving a person
and a location and there is a proposition
about some person in that location Then store
that person and location as the retrieved
pair. Mismatch-Person If the retrieved person
mismatches the probe Then say no. Mismatch-Locati
on If the retrieved location mismatches the
probe Then say no. Match-Both If the retrieved
person and location both match the probe Then say
yes.
Web Address ACT-R Home Page
Published ACT-R Models Atomic
Components of Thought Chapter 3
Fan Effect Model
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Fan Effect
39
Threshold ?
Chunks with an activation lower than threshold ?
can not be retrieved
1
Retrieval probability
(A- ?)/s
Equivalently Odds of recall e
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Partial matching
Errors of Omission
These occur when the correct chunk falls below
the activation threshold for retrieval and the
intended production rule therefore cannot fire.
gt
Errors of Commission
These occur when some wrong chunk is retrieved
instead of the correct one and so the wrong
instantiation fires.
gt
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Partial matching
partial matching is restricted to chunks with the
same type as specified in a productions
retrieval pattern
an amount reflecting the degree of mismatch Dip
to a retrieval pattern of production p is
subtracted from the activation level Ai of a
partially matching chunk i. The match score for
the match of chunk i to production p is
Mip Ai - Dip
Dip is the sum for each slot of the degree of
mismatch between the value of the slot in chunk i
and the respective retrieval pattern
Probability of retrieving chunk i as a match for
production p
Mip/t
e
t ?6 ???? ?2 s
Mjp/t
?
e
j
42
SUGAR FACTORY
43
SUGAR FACTORY
Sugar productiont 2 workerst - sugar
productiont-1 /- 1000
44
Similarities example
Ratio Similarities
D Mismatch Penalty (1-sim(a, b))
45
Retrieval of encoded chunks
Lebiere, C., Wallach, D. Taatgen, N. (1998).
Implicit and explicit learning in ACT-R. In F.
E. Ritter And R. Young (Eds.) Proceedings of the
Second European Conference on Cognitive Modeling,
pp. 183-189. Nottingham Nottingham University
Press.
46
Control performance
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Concordance
48
Transition from computation to retrieval
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Conflict resolution
In general, conflict resolution gives answers to
two questions
Which production out of a set of matching
productions is selected?
Which instantiation of the selected production is
fired?
50
Conflict resolution

G
C
P

Expected Gain
Probability of goal achievement
Cost of goal achievement
Goal value
goal-specific
production-specific
51
Selection of Productions
G
P
C


Expected Gain
Probability of goal achievement
Cost of goal achievement
Goal value
q
r
a

b

52
Probability of Goal Achievement
P
q
r

probability of the production working
successfully
probability of achieving the goal if the
production works successfully
Production's matching/actions/subgoals
Goal accomplished and popped have the intended
effect successfully.
Achieving a goal depends on the joint probability
of the respective production being successful and
subsequent rules eventually reaching the goal.
53
Costs of a production
C
a
b

estimate of the amount of effort from when
a pro- duction completes until the goal
is achieved
amount of effort (in time) that a pro-
duction will take
Production's costs of matching/actions/subgoals
Costs of future productions
Production costs are calculated as the sum of the
effort associated with production pi and (an
estimate of) the effort that subsequent
productions pj..n take on the way to goal
achievement.
54
Conflict resolution
P

q
r


Intended next state

current state
goal state


a
b

C
55
Goal value
G20
p3
!push!
G'17
G' rG-b .9 20 - 1 17
ACT-R values a goal less the more deeply it is
embedded in uncertain subgoals
ACT-R pops the goal with failure if no production
above the utility threshold (default 0) can
match (goal abandonment)
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Noise in Conflict Resolution
Remember
Evaluation Ei of production i P(i)G-C(i)
Boltzmann Equation
Ei/t
e
Probability of choosing i among n
applicable productions with Evaluation Ej
Ej/t
?
e
j
?2
t
57
2-person Matrix Game
Players
Actions
Payoff matrix
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Data sets
Erev Roth (1998)
There is a danger that investigators will treat
the models like their toothbrushes, and each
will use its own model only on his own data.
Diverse data sets re-analyzed
Suppes Atkinson (1960) SA2, SA8, SA3k,
SA3u Erev Roth (1998)
SA3n Malcom Liebermann (1965) O'Neill
(1987) Rapoport Boebel (1992) RB10, RB15
2 x 2 4 x 4 5 x 5
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Model
(p player1-B goalgt isa decide player1
nil gt goalgt player1 B )
(p player1-A goalgt isa decide player1
nil gt goalgt player1 A )
Productions
Chunk
game12 isa decide player1 A player2 B
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2 4 6 0 3 3 1 5
1/3 2/3 1 0 1/2 1/2 1/6 5/6
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Best Fits Random Games
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Conflict resolution
test goal pattern
Goal
(1)
Match
Ep 13.95
(2)
evaluate conflict set
Ep 18.95
Ep 17.30
selection
(3)
Ep 18.95
retrieve chunk(s)
Match
fire production
(4)
63
Learning as Subsymbolic Tuning to the Statistics
of the Environment
1. Lael Schooler Statistical structure of the
demands on declarative memory posed by the
environment. 2. Christian Lebiere Consequences
for 20 years of practicing arithmetic facts. 3.
Marsha Lovett Selection among production rules
is also sensitive to both the features of the
current problem and the rules past history of
success.
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-.73
Odds .14 T
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-.77
Odds .18 T
68
-.83
Odds .34 T
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Parameter learning
n
log(S tj-d)
j1
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Environmental Analyses of Context and Recency
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Lael Schooler Retrieval Odds Mirrors Odds of
Occurring
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Conclusions from Environmental Studies
Log Odds Log Proposal for ACT-Rs
Declarative Memory - Activation reflects Log
Odds of Occurring - Learning works as
a Bayesian inference scheme to try to identify
the right values of the factors determining odds
of recall.
Context
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Declarative Equations
78
Retrieve
Compute
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Problem Size Effect over Time
Model
80
Effect of Argument Size on Accuracy For Addition
(4 year olds)
Data
Model
Percentage of Correct Retrieval per Operand
Percentage Correct in Simulation
81
Effect of Argument Size on Accuracy For
Multiplication (3rd Grade)
Data
Model
Percentage of Correct Computations per Operand
Percentage Errors in Multiplication
Simulation
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Procedural Learning
P is expected probability of success G is value
of goal C is expected cost
t reflects noise in evaluation and is like
temperature in the Bolztman equation
a is prior successes m is experienced successes b
is prior failures n is experienced failures
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Building Sticks Task (Lovett)
85
Lovett Anderson, 1996
(2/3)
(5/6)
86
Build Sticks Demo
Web Address ACT-R Home Page Published
ACT-R Models Atomic Components of
Thought Chapter 4
Building Sticks Model
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Decay of Experience
Note Such temporal weighting is critical in the
real world.
89
Credit-Assignment in ACT-R
90
Building Sticks Task 2 Levels
75
75
75
91
Choice Learning
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Adapting to a Variable and Changing World
It would be trivial to create a system that would
do well at this task simply by eliminating the
noise and getting rid of the discounting of past
experience. However, this again makes the error
of assuming that the human mind evolved for
optimal performance at our particular laboratory
task. In the real world noise is important
both to explore other options and to avoid
getting caught in traps. The discounting of
experience also allows us to rapidly update in
the presence of the changing world. Christian
Lebiere and Robert West have shown that these
features are critical to getting good performance
in games as simple as rocks-papers-scissors.
93
ACT-R/PM
94
Martin-Emerson-Wickens Task
Perform compensatory tracking, keeping the
crosshair on target Respond to choice stimuli
as rapidly as possible Choice stimulus appears
at various distances from target (vertical
separation) Tracking requires eye to be on the
crosshair Eye must be moved to see stimulus
Choice response tracking move- ments are
bottlenecked through single motor module
(Dual-) Task
Model
Martin-Emerson Wickens (1992) The vertical
visual field and implications for the
head-up display
95
MEW Productions
Find-Target-Oval IF the target hasn't been
located and the oval is at location THEN
mark the target at location Attend-Cursor IF
the target has been found and the state has not
been set and the pointer is at location
and has not been attended to and the
vision module is free THEN send a command to move
the attention to location and set the
state as "looking" Attend-Cursor-Again IF
the target has been found and the state is
"looking" and the pointer is at location
and has not been attended to and the
vision module is free THEN send a command to move
the attention to location Start-Tracking IF
the state is "looking" and the object
focused on is a pointer and the vision
module is free THEN send a command to track the
pointer and update the state to "tracking"
96
Move-Cursor IF the state is "tracking" and
the target is at location and the motor
module is free THEN send a command to move the
cursor to location Stop-Tracking IF the
state is "tracking" and there is an
arrow on screen that hasn't been
attended to THEN move the attention to that
location and update the state to
"arrow" Right-Arrow IF the state is
"arrow" and the arrow is pointing to
the right and the motor module is
free THEN send a command to punch the left index
finger and clear the state Left-Arrow
IF the state is "arrow" and the
arrow is pointing to the left and the
motor module is free THEN send a command to punch
the left middle finger and clear the
state
97
Schedule chart for Schumacher, et al. (1997)
perfect time-sharing model. VM visual- Manual
ask, AV auditory-verbal task, RS response
selection.
98
ACT-R/PM simulation of Schumacher, et al. (1997)
perfect time-sharing results.