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Introduction to ACT-R 5. 0 Tutorial 24 th Annual Conference Cognitive Science Society Christian Lebiere Human Computer Interaction Institute Carnegie Mellon University Pittsburgh, PA 15213 [email protected] edu ACT-R Home Page: http: //act. psy. cmu. edu
Tutorial Overview 1. Introduction 2. Symbolic ACT-R Declarative Representation: Chunks Procedural Representation: Productions ACT-R 5. 0 Buffers: A Complete Model for Sentence Memory 3. Chunk Activation in ACT-R Activation Calculations Spreading Activation: The Fan Effect Partial Matching: Cognitive Arithmetic Noise: Paper Rocks Scissors Base-Level Learning: Paired Associate 4. Production Utility in ACT-R Principles and Building Sticks Example 5. Production Compilation Principles and Successes 6. Predicting f. MRI BOLD response Principles and Algebra example
Motivations for a Cognitive Architecture 1. Philosophy: Provide a unified understanding of the mind. 2. Psychology: Account for experimental data. 3. Education: Provide cognitive models for intelligent tutoring systems and other learning environments. 4. Human Computer Interaction: Evaluate artifacts and help in their design. 5. Computer Generated Forces: Provide cognitive agents to inhabit training environments and games. 6. Neuroscience: Provide a framework for interpreting data from brain imaging.
Approach: Integrated Cognitive Models t Cognitive model = computational process that thinks/acts like a person t Integrated cognitive models Driver Model … User Model • • •
Study 1: Dialing Times t Total time to complete dialing Model Predictions Human Data
Study 1: Lateral Deviation t Deviation from lane center (RMSE) Model Predictions Human Data
These Goals for Cognitive Architectures Require 1. Integration, not just of different aspects of higher level cognition but of cognition, perception, and action. 2. Systems that run in real time. 3. Robust behavior in the face of error, the unexpected, and the unknown. 4. Parameter-free predictions of behavior. 5. Learning.
History of the ACT-framework Predecessor HAM (Anderson & Bower 1973) Theory versions ACT-E ACT* ACT-R 4. 0 ACT-R 5. 0 (Anderson, 1976) (Anderson, 1978) (Anderson, 1993) (Anderson & Lebiere, 1998) (Anderson & Lebiere, 2001) Implementations GRAPES PUPS ACT-R 2. 0 ACT-R 3. 0 ACT-R 4. 0 ACT-R/PM ACT-R 5. 0 Windows Environment Macintosh Environment (Sauers & Farrell, 1982) (Anderson & Thompson, 1989) (Lebiere & Kushmerick, 1993) (Lebiere, 1995) (Lebiere, 1998) (Byrne, 1998) (Lebiere, 2001) (Bothell, 2001) (Fincham, 2001)
~ 100 Published Models in ACT-R 1997 -2002 III. Problem Solving & Decision Making I. Perception & Attention 1. Tower of Hanoi 1. Psychophysical Judgements 2. Choice & Strategy Selection 2. Visual Search 3. Mathematical Problem Solving 3. Eye Movements 4. Spatial Reasoning 4. Psychological Refractory Period 5. Dynamic Systems 5. Task Switching 6. Use and Design of Artifacts 6. Subitizing 7. Game Playing 7. Stroop 8. Insight and Scientific Discovery 8. Driving Behavior 9. Situational Awareness IV. Language Processing 10. Graphical User Interfaces 1. Parsing 2. Analogy & Metaphor II. Learning & Memory 3. Learning 1. List Memory 4. Sentence Memory 2. Fan Effect 3. Implicit Learning V. Other 4. Skill Acquisition 1. Cognitive Development 5. Cognitive Arithmetic 2. Individual Differences 6. Category Learning 3. Emotion 7. Learning by Exploration 4. Cognitive Workload and Demonstration 5. Computer Generated Forces 8. Updating Memory & 6. f. MRI Prospective Memory 7. Communication, Negotiation, 9. Causal Learning Group Decision Making Visit http: //act. psy. cmu. edu/papers/ACT-R_Models. htm link.
ACT-R 5. 0 Intentional Module (not identified) Declarative Module (Temporal/Hippocampus) Productions (Basal Ganglia) Goal Buffer (DLPFC) Retrieval Buffer (VLPFC) Matching (Striatum) Selection (Pallidum) Execution (Thalamus) Visual Buffer (Parietal) Visual Module (Occipital/etc) Manual Buffer (Motor) Manual Module (Motor/Cerebellum) Environment
ACT-R: Knowledge Representation goal buffer visual buffer retrieval buffer
ACT-R: Assumption Space
Chunks: Example ( CHUNK-TYPE NAME SLOT 1 (F SLOT 2 SLOTN ACT 3+4 isa ADDITION-FACT ADDEND 1 THREE ADDEND 2 FOUR SUM SEVEN ) )
Chunks: Example (CLEAR-ALL) (CHUNK-TYPE addition-fact addend 1 addend 2 sum) (CHUNK-TYPE integer value) (ADD-DM (fact 3+4 isa addition-fact addend 1 three addend 2 four sum seven) (three isa integer value 3) (four isa integer value 4) (seven isa integer value 7)
Chunks: Example ADDITION-FACT 3 VALUE 7 isa ADDEND 1 THREE VALUE SUM FACT 3+4 SEVEN ADDEND 2 isa FOUR isa INTEGER 4 VALUE isa
Chunks: Exercise I Fact: The cat sits on the mat. Encoding: proposition (Chunk-Type proposition agent action object) (Add-DM (fact 007 isa proposition agent cat 007 action sits_on object mat) ) isa cat 007 agent fact 007 action sits_on object mat
Chunks: Exercise II The black cat with 5 legs sits on the mat. Fact Chunks (Chunk-Type proposition agent action object) (Chunk-Type cat legs color) cat (Add-DM (fact 007 isa proposition agent cat 007 action sits_on object mat) (cat 007 isa cat legs 5 color black) proposition isa legs 5 cat 007 fact 007 agent color ) black object action sits_on mat
Chunks: Exercise III (Chunk-Type proposition agent action object) (Chunk-Type prof money-status age) (Chunk-Type house kind price status) Fact The rich young professor buys a beautiful and expensive city house. proposition prof agent money- prof 08 status age young house isa rich Chunk fact 008 action buys expensive price isa object status beautiful obj 1001 kind city-house (Add-DM (fact 008 isa proposition agent prof 08 action buys object house 1001 ) (prof 08 isa prof money-status rich age young ) (obj 1001 isa house kind city-house price expensive status beautiful ) )
A Production is 1. The greatest idea in cognitive science. 2. The least appreciated construct in cognitive science. 3. A 50 millisecond step of cognition. 4. The source of the serial bottleneck in otherwise parallel system. 5. A condition-action data structure with “variables”. 6. A formal specification of the flow of information from cortex to basal ganglia and back again.
Productions • • Key Properties Structure of productions ( p modularity abstraction goal/buffer factoring conditional asymmetry name Specification of Buffer Tests condition part delimiter ==> action part ) Specification of Buffer Transformations
ACT-R 5. 0 Buffers 1. Goal Buffer (=goal, +goal) -represents where one is in the task -preserves information across production cycles 2. Retrieval Buffer (=retrieval, +retrieval) -holds information retrieval from declarative memory -seat of activation computations 3. Visual Buffers -location (=visual-location, +visual-location) -visual objects (=visual, +visual) -attention switch corresponds to buffer transformation 4. Auditory Buffers (=aural, +aural) -analogous to visual 5. Manual Buffers (=manual, +manual) -elaborate theory of manual movement include feature preparation, Fitts law, and device properties 6. Vocal Buffers (=vocal, +vocal) -analogous to manual buffers but less well developed
Model for Anderson (1974) Participants read a story consisting of Active and Passive sentences. Subjects are asked to verify either active or passive sentences. All Foils are Subject-Object Reversals. Predictions of ACT-R model are “almost” parameter-free. DATA: Targets: Foils: Studied-form/Test-form Active-active Active-passive Passive-active Passive-passive 2. 25 2. 80 2. 30 2. 75 2. 55 2. 95 Predictions: Targets: Foils: Active-active Active-passive Passive-active Passive-passive 2. 36 2. 86 2. 51 3. 01 CORRELATION: 0. 978 MEAN DEVIATION: 0. 072
250 m msec in the life of ACT-R: Reading the Word “The” Identifying Left-most Location Time 63. 900: Find-Next-Word Selected Time 63. 950: Find-Next-Word Fired Time 63. 950: Module : VISION running command FIND-LOCATION Attending to Word Time 63. 950: Time 64. 000: Time 64. 050: Attend-Next-Word Selected Attend-Next-Word Fired Module : VISION running command MOVE-ATTENTION Module : VISION running command FOCUS-ON Encoding Word Time 64. 050: Read-Word Selected Time 64. 100: Read-Word Fired Time 64. 100: Failure Retrieved Skipping The Time 64. 100: Skip-The Selected Time 64. 150: Skip-The Fired
Attending to a Word in Two Productions (P find-next-word =goal> ISA comprehend-sentence word nil ==> +visual-location> ISA visual-location screen-x lowest attended nil =goal> word looking ) (P attend-next-word =goal> ISA comprehend-sentence word looking =visual-location> ISA visual-location ==> =goal> word attending +visual> ISA visual-object screen-pos =visual-location ) no word currently being processed. find left-most unattended location update state looking for a word visual location has been identified update state attend to object in that location
Processing “The” in Two Productions (P read-word =goal> ISA comprehend-sentence word attending =visual> ISA text value =word status nil ==> =goal> word =word +retrieval> ISA meaning word =word ) (P skip-the =goal> ISA comprehend-sentence word "the" ==> =goal> word nil ) attending to a word has been identified hold word in goal buffer retrieve word’s meaning the word is “the” set to process next word
Processing “missionary” in 450 msec. Identifying left-most unattended Location Time 64. 150: Find-Next-Word Selected Time 64. 200: Find-Next-Word Fired Time 64. 200: Module : VISION running command FIND-LOCATION Attending to Word Time 64. 200: Attend-Next-Word Selected Time 64. 250: Attend-Next-Word Fired Time 64. 250: Module : VISION running command MOVE-ATTENTION Time 64. 300: Module : VISION running command FOCUS-ON Encoding Word Time 64. 300: Read-Word Selected Time 64. 350: Read-Word Fired Time 64. 550: Missionary Retrieved Processing the First Noun Time 64. 550: Process-First-Noun Selected Time 64. 600: Process-First-Noun Fired
" src="https://present5.com/presentation/f1c555d5236ab21d985ea32db33ac0b1/image-27.jpg" alt="Processing the Word “missionary” Missionary 0. 000 isa MEANING word "missionary" (P process-first-noun =goal>" /> Processing the Word “missionary” Missionary 0. 000 isa MEANING word "missionary" (P process-first-noun =goal> ISA comprehend-sentence neither agent or action agent nil has been assigned action nil word =y =retrieval> word meaning has been ISA meaning retrieved word =y ==> =goal> assign meaning to agent =retrieval and set to process next word nil )
Three More Words in the life of ACT-R: 950 msec. Processing “was” Time Time Time 64. 600: 64. 650: 64. 700: 64. 750: 64. 800: 64. 850: Find-Next-Word Selected Find-Next-Word Fired Module : VISION running command FIND-LOCATION Attend-Next-Word Selected Attend-Next-Word Fired Module : VISION running command MOVE-ATTENTION Module : VISION running command FOCUS-ON Read-Word Selected Read-Word Fired Failure Retrieved Skip-Was Selected Skip-Was Fired Processing “feared” Time Time Time 64. 850: 64. 900: 64. 950: 65. 000: 65. 050: 65. 250: 65. 300: Find-Next-Word Selected Find-Next-Word Fired Module : VISION running command FIND-LOCATION Attend-Next-Word Selected Attend-Next-Word Fired Module : VISION running command MOVE-ATTENTION Module : VISION running command FOCUS-ON Read-Word Selected Read-Word Fired Fear Retrieved Process-Verb Selected Process-Verb Fired Processing “by” Time Time Time 65. 300: 65. 350: 65. 400: 65. 450: 65. 500: 65. 550: Find-Next-Word Selected Find-Next-Word Fired Module : VISION running command FIND-LOCATION Attend-Next-Word Selected Attend-Next-Word Fired Module : VISION running command MOVE-ATTENTION Module : VISION running command FOCUS-ON Read-Word Selected Read-Word Fired Failure Retrieved Skip-By Selected Skip-By Fired
Reinterpreting the Passive (P skip-by =goal> ISA word agent ==> =goal> word object agent ) comprehend-sentence "by" =per nil
Two More Words in the life of ACT-R: 700 msec. Processing “the” Time 65. 550: Find-Next-Word Selected Time 65. 600: Find-Next-Word Fired Time 65. 600: Module : VISION running command FIND-LOCATION Time 65. 600: Attend-Next-Word Selected Time 65. 650: Attend-Next-Word Fired Time 65. 650: Module : VISION running command MOVE-ATTENTION Time 65. 700: Module : VISION running command FOCUS-ON Time 65. 700: Read-Word Selected Time 65. 750: Read-Word Fired Time 65. 750: Failure Retrieved Time 65. 750: Skip-The Selected Time 65. 800: Skip-The Fired Processing “cannibal” Time 65. 800: Find-Next-Word Selected Time 65. 850: Find-Next-Word Fired Time 65. 850: Module : VISION running command FIND-LOCATION Time 65. 850: Attend-Next-Word Selected Time 65. 900: Attend-Next-Word Fired Time 65. 900: Module : VISION running command MOVE-ATTENTION Time 65. 950: Module : VISION running command FOCUS-ON Time 65. 950: Read-Word Selected Time 66. 000: Read-Word Fired Time 66. 200: Cannibal Retrieved Time 66. 200: Process-Last-Word-Agent Selected Time 66. 250: Process-Last-Word-Agent Fired
Retrieving a Memory: 250 msec Time 66. 250: Retrieve-Answer Selected Time 66. 300: Retrieve-Answer Fired Time 66. 500: Goal 123032 Retrieved (P retrieve-answer =goal> ISA comprehend-sentence agent =agent action =verb object =object purpose test ==> =goal> purpose retrieve-test +retrieval> ISA comprehend-sentence action =verb purpose study ) sentence processing complete update state retrieve sentence involving verb
Generating a Response: 410 ms. Time Time 66. 500: 66. 700: 66. 850: 66. 910: Answer-No Selected Answer-No Fired Module : MOTOR running command PRESS-KEY Module : MOTOR running command PREPARATION-COMPLETE Device running command OUTPUT-KEY (P answer-no =goal> ISA comprehend-sentence agent =agent action =verb object =object purpose retrieve-test =retrieval> ISA comprehend-sentence - agent =agent action =verb - object =object purpose study ==> =goal> purpose done +manual> ISA press-key "d" ) ready to test retrieve sentence does not match agent or object update state indicate no
Subsymbolic Level The subsymbolic level reflects an analytic characterization of connectionist computations. These computations have been implemented in ACT-RN (Lebiere & Anderson, 1993) but this is not a practical modeling system. 1. Production Utilities are responsible for determining which productions get selected when there is a conflict. 2. Production Utilities have been considerably simplified in ACT-R 5. 0 over ACT-R 4. 0. 3. Chunk Activations are responsible for determining which (if any chunks) get retrieved and how long it takes to retrieve them. 4. Chunk Activations have been simplified in ACT-R 5. 0 and a major step has been taken towards the goal of parameter-free predictions by fixing a number of the parameters. As with the symbolic level, the subsymbolic level is not a static level, but is changing in the light of experience. Subsymbolic learning allows the system to adapt to the statistical structure of the environment.
Activation Seven Sum Three Addend 1 Chunk i Bi Addend 2 Four Sji =Goal> isa write + relation sum Conditions arg 1 Three arg 2 Four +Retrieval> + isa addition-fact addend 1 Three Actions addend 2 Four Sim kl
Chunk Activation activation ( base = activation+ )( associative source activation* strength + mismatch penalty * ) similarity value + noise 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 Associative Activation: relevance to the general context Matching Penalty: relevance to the specific match required Noise: stochastic is useful to avoid getting stuck in local minima
Activation, Latency and Probability • Retrieval time for a chunk is a negative exponential function of its activation: • Probability of retrieval of a chunk follows the Boltzmann (softmax) distribution: • The chunk with the highest activation is retrieved provided that it reaches the retrieval threshold • For purposes of latency and probability, the threshold can be considered as a virtual chunk
Base-level Activation activation Ai base = activation = Bi The base level activation Bi of chunk Ci reflects a contextindependent 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 P(Ci) Bi = ln ( P(C ) ) i
Source Activation + + ( * source activation W j j associative strength * ) Sji 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 source activation W= Wj reflects an individual difference parameter.
Associative Strengths + ( * source activation W + j associative strength * ) 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 ( P(Ni Cj) P(Ni) ) = S - ln(P(Ni|Cj))
Application: Fan Effect
Partial Matching ( + mismatch penalty * ) similarity value • The mismatch penalty is a measure of the amount of control over memory retrieval: MP = 0 is free association; MP very large means perfect matching; intermediate values allow some mismatching in search of a memory match. • Similarity values between desired value k specified by the production and actual value l present in the retrieved chunk. This provides generalization properties similar to those in neural networks; the similarity value is essentially equivalent to the dot-product between distributed representations.
Application: Cognitive Arithmetic
Noise + noise • Noise provides the essential stochasticity of human behavior • Noise also provides a powerful way of exploring the world • Activation noise is composed of two noises: • A permanent noise accounting for encoding variability • A transient noise for moment-to-moment variation
Application: Paper Rocks Scissors (Lebiere & West, 1999) • Too little noise makes the system too deterministic. • Too much noise makes the system too random. • This is not limited to game-playing situations!
Base-Level Learning Based on the Rational Analysis of the Environment (Schooler & Anderson, 1997) Base-Level Activation reflects the log-odds that a chunk will be needed. In the environment the odds that a fact will be needed decays as a power function of how long it has been since it has been used. The effects of multiple uses sum in determining the odds of being used. Base-Level Learning Equation ≈ n(n / (1 -d)) - d*n(L) Note: The decay parameter d has been set to. 5 in most ACT-R models
Paired Associate: Study Time Time Time 5. 000: Find Selected 5. 050: Module : VISION running command FIND-LOCATION 5. 050: Find Fired 5. 050: Attend Selected 5. 100: Module : VISION running command MOVE-ATTENTION 5. 100: Attend Fired 5. 150: Module : VISION running command FOCUS-ON 5. 150: Associate Selected 5. 200: Associate Fired (p associate =goal> isa goal arg 1 =stimulus step attending state study =visual> isa text value =response status nil ==> =goal> isa goal arg 2 =response step done +goal> isa goal state test step waiting) attending word during study visual buffer holds response store response in goal with stimulus prepare for next trial
Paired Associate: Successful Recall Time Time Time Time 10. 000: 10. 050: 10. 100: 10. 150: 10. 200: 10. 462: 10. 512: 10. 762: 10. 912: Find Selected Module : VISION running command FIND-LOCATION Find Fired Attend Selected Module : VISION running command MOVE-ATTENTION Attend Fired Module : VISION running command FOCUS-ON Read-Stimulus Selected Read-Stimulus Fired Goal Retrieved Recall Selected Module : MOTOR running command PRESS-KEY Recall Fired Module : MOTOR running command PREPARATION-COMPLETE Device running command OUTPUT-KEY
Paired Associate: Successful Recall (cont. ) (p read-stimulus =goal> isa goal step attending state test =visual> isa text value =val ==> +retrieval> isa goal relation associate arg 1 =val =goal> isa goal relation associate arg 1 =val step testing) (p recall =goal> isa goal relation associate arg 1 =val step testing =retrieval> isa goal relation associate arg 1 =val arg 2 =ans ==> +manual> isa press-key =ans =goal> step waiting)
Paired Associate Example Data Trial 1 2 3 4 5 6 7 8 Accuracy. 000. 526. 667. 798. 887. 924. 958. 954 Predictions Latency 0. 000 2. 156 1. 967 1. 762 1. 680 1. 552 1. 467 1. 402 Trial 1 2 3 4 5 6 7 8 Accuracy. 000. 515. 570. 740. 850. 865. 895. 930 Latency 0. 000 2. 102 1. 730 1. 623 1. 584 1. 508 1. 552 1. 462 ? (collect-data 10) Note simulated runs show random fluctuation. ACCURACY (0. 0 0. 515 0. 570 0. 740 0. 850 0. 865 0. 895 0. 930) CORRELATION: 0. 996 MEAN DEVIATION: 0. 053 LATENCY (0 2. 102 1. 730 1. 623 1. 589 1. 508 1. 552 1. 462) CORRELATION: 0. 988 MEAN DEVIATION: 0. 112 NIL
Production Utility 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
Building Sticks Task (Lovett)
Lovett & Anderson, 1996 (2/3) (5/6)
Building Sticks Demo Web Address: ACT-R Home Page Published ACT-R Models Atomic Components of Thought Chapter 4 Building Sticks Mod
Decay of Experience Note: Such temporal weighting is critical in the real world.
Production Compilation: The Basic Idea (p read-stimulus =goal> isa goal step attending state test =visual> isa text value =val ==> +retrieval> isa goal relation associate arg 1 =val arg 2 =ans =goal> relation associate arg 1 =val step testing) (p recall =goal> isa goal relation associate arg 1 =val step testing =retrieval> isa goal relation associate arg 1 =val arg 2 =ans ==> +manual> isa press-key =ans =goal> step waiting) (p recall-vanilla =goal> isa goal step attending state test =visual> isa text value "vanilla ==> +manual> isa press-key "7" =goal> relation associate arg 1 "vanilla" step waiting)
Production Compilation: The Principles 1. Perceptual-Motor Buffers: Avoid compositions that will result in jamming when one tries to build two operations on the same buffer into the same production. 2. Retrieval Buffer: Except for failure tests proceduralize out and build more specific productions. 3. Goal Buffers: Complex Rules describing merging. 4. Safe Productions: Production will not produce any result that the original productions did not produce. 5. Parameter Setting: Successes = P*initial-experience* Failures = (1 -P) *initial-experience* Efforts = (Successes + Efforts)(C + *cost-penalty*)
Production Compilation: The Successes 1. Taatgen: Learning of inflection (English past and German plural). Shows that production compilation can come up with generalizations. 2. Taatgen: Learning of air-traffic control task – shows that production compilation can deal with complex perceptual motor skill. 3. Anderson: Learning of productions for performing paired associate task from instructions. Solves mystery of where the productions for doing an experiment come from. 4. Anderson: Learning to perform an anti-air warfare coordinator task from instructions. Shows the same as 2 & 3. 5. Anderson: Learning in the fan effect that produces the interaction between fan and practice. Justifies a major simplification in the parameterization of productions – no strength separate from utility. Note all of these examples involve all forms of learning occurring in ACT-R simultaneous – acquiring new chunks, acquiring new productions, activation learning, and utility learning.
Predicting f. MRI Bold Response from Buffer Activity Example: Retrieval buffer during equation-solving predicts activity in left dorsolateral prefrontal cortex. where Di is the duration of the ith retrieval and ti is the time of initiation of the retrieval.
21 Second Structure of f. MRI Trial Load a=18 b=6 c=5 Equation cx+3=a 1. 5 Second Scans Blank Period
Solving 5 x + 3 = 18 Time Time Time Time Time Time Time 3. 000: Find-Right-Term Selected 3. 050: Find-Right-Term Fired 3. 050: Module : VISION running command FIND- Time 3. 050: Attend-Next-Term-Equation Selected 3. 100: Attend-Next-Term-Equation Fired 3. 100: Module : VISION running command MOVE- Time 3. 150: Module : VISION running command FOCUS-ON 3. 150: Encode Selected 3. 200: Encode Fired 3. 281: 18 Retrieved 3. 281: Process-Value-Integer Selected 3. 331: Process-Value-Integer Fired 3. 331: Module : VISION running command FIND- Time 3. 331: Attend-Next-Term-Equation Selected 3. 381: Attend-Next-Term-Equation Fired 3. 381: Module : VISION running command MOVE- Time 3. 431: Module : VISION running command FOCUS-ON 3. 431: Encode Selected 3. 481: Encode Fired 3. 562: 3 Retrieved 3. 562: Process-Op 1 -Integer Selected 3. 612: Process-Op 1 -Integer Fired 3. 612: Module : VISION running command FIND- Time 3. 612: Attend-Next-Term-Equation Selected 3. 662: Attend-Next-Term-Equation Fired 3. 662: Module : VISION running command MOVE- Time 3. 712: Module : VISION running command FOCUS-ON 3. 712: Encode Selected 3. 762: Encode Fired 4. 362: Inverse-of-+ Retrieved 4. 362: Process-Operator Selected
Solving 5 x + 3 = 18 (cont. ) Time 4. 412: Process-Operator Fired Time 5. 012: F 318 Retrieved Time 5. 012: Finish-Operation 1 Selected Time 5. 062: Finish-Operation 1 Fired Time 5. 062: Module : VISION running command FIND- Time 5. 062: Attend-Next-Term-Equation Selected Time 5. 112: Attend-Next-Term-Equation Fired Time 5. 112: Module : VISION running command MOVETime 5. 162: Module : VISION running command FOCUS-ON Time 5. 162: Encode Selected Time 5. 212: Encode Fired Time 5. 293: 5 Retrieved Time 5. 293: Process-Op 2 -Integer Selected Time 5. 343: Process-Op 2 -Integer Fired Time 5. 943: F 315 Retrieved Time 5. 943: Finish-Operation 2 Selected Time 5. 993: Finish-Operation 2 Fired Time 5. 993: Retrieve-Key Selected Time 6. 043: Retrieve-Key Fired Time 6. 124: 3 Retrieved Time 6. 124: Generate-Answer Selected Time 6. 174: Generate-Answer Fired Time 6. 174: Module : MOTOR running command PRESS-KEY Time 6. 424: Module : MOTOR running command PREPARATION- Time 6. 574: Device running command OUTPUT-KEY ("3" 3. 574)
Left Dorsolateral Prefrontal Cortex
Bold Response for 2 Equation Types Left Dorsolateral Prefrontal Cortex 0. 6 0. 5 Percent Activation Change 5 x + 3 = 18 0. 4 cx + 3 = a 0. 3 0. 2 0. 1 0. 0 -0. 1 1 2 3 4 5 6 7 8 Scan (1. 5 sec. ) 9 10 11 12 13 14