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Introduction to ACT-R Tutorial 21st Annual Conference Cognitive Science Society

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+@cmu.edu cl+@cmu.edu. Dieter Wallach

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Introduction to ACT-R Tutorial 21st Annual Conference Cognitive Science Society

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  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+@cmu.edu cl+@cmu.edu Dieter Wallach Institut fur Psychologie Universitaet Basel Bernoullistr. 16 CH-4056 Basel wallachd@ubaclu.unibas.ch

  2. Tutorial Overview 1. Introduction 2. Symbolic ACT-R Declarative Procedural 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.

  3. 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. Newell’s 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

  5. 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

  6. 13. Hierarchical problem solving tasks including Tower of Hanoi 14. Strategy selectionincluding 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.

  7. History of the ACT-framework Predecessor HAM (Anderson & Bower 1973) Theory versions ACT-E (Anderson, 1976) ACT* (Anderson, 1978) ACT-R (Anderson, 1993) ACT-R 4.0 (Anderson & Lebiere, 1998) ImplementationsGRAPES (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)

  8. ACT-R: Information Flow ACT-R : Information Flow

  9. ACT-R: Knowledge Representation

  10. ACT-R: Assumption Space

  11. Chunks: Example ( ) CHUNK-TYPE NAME SLOT1 SLOT2 SLOTN ( ( NEWCHUNK FACT3+4 NAME ADDITION-FACT isa isa SLOT1 Filler1 ADDEND1 THREE SLOT2 Filler2 ADDEND2 FOUR ) ) SLOTN FillerN SUM SEVEN

  12. Chunks: Example (CLEAR-ALL) (CHUNK-TYPE addition-fact addend1 addend2 sum) (CHUNK-TYPE integer value) (ADD-DM (fact3+4 isa addition-fact addend1 three addend2 four sum seven) (three isa integer value 3) (four isa integer value 4) (seven isa integer value 7)

  13. Chunks: Example ADDITION-FACT 3 7 VALUE isa VALUE ADDEND1 SUM THREE SEVEN FACT3+4 ADDEND2 4 isa isa FOUR VALUE isa INTEGER

  14. Encoding: (Chunk-Type proposition agent action object) 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

  15. Chunks • (Chunk-Type proposition agent action object) • (Chunk-Type cat legs color) • (Add-DM • (fact007 isa proposition • agent cat007 • action sits_on • object mat) • (cat007 isa cat • legs 5 • color black) • ) Chunks: Exercise II Fact The black cat with 5 legs sits on the mat. cat proposition isa isa legs 5 cat007 fact007 mat agent object color action black sits_on

  16. 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 status kind action age beautiful city-house young buys

  17. Productions set of productions, organized through reference to goals procedural memory • modularity • abstraction • goal factoring • conditional asymmetry productions Structure of productions ( p name <Goal pattern> <Chunk retrieval> condition part delimiter ==> <Goal Transformation> <External action> action part )

  18. 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.

  20. Add-numbers production name (p add-numbers =goal> isa add-column num1 =add1 num2 =add2 result nil =fact> isa addition-fact addend1 =add1 addend2 =add2 sum =sum = => =goal> result =sum ) goal pattern head/slot separator = fact > chunk retrieval variable prefix action description

  21. (p add-numbers =goal> isa add-column num1 =add1 num2 =add2 result nil =fact> isa addition-fact addend1 =add1 addend2 =add2 sum =sum = = > =goal> result =sum ) (first-goal isa add-colomn num1 three num2 four result nil) (fact3+4 isa addition-fact addend1 three addend2 four sum seven) (first-goal isa add-colomn num1 three num2 four result seven) 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

  22. Pattern matching left-hand side =goal> isa find-sum addend2 =num2 sum =sum negation =fact> isa add-fact addend1 zero addend2 =num2 sum =sum — addend1 goal (goal1 isa find-sum addend1 nil addend2 two sum four ) declarative memory (fact2+3 isa add-fact addend1 two addend2 three sum five) (fact3+1 isa add-fact addend1 three addend2 one sum four) (fact0+4 isa add-fact addend1 zero addend2 four sum four) (fact2+2 isa add-fact addend1 two addend2 two sum four)

  23. Counting Example Web Address: ACT-R Home Page Published ACT-R Models Counting Example

  24. !push! =G3 Goal Stack G3 G4 G2 G1 G2 G1 G1 G1 !push! =G2 !focus-on! =G4 !pop! Initial state stack-manipulating actions

  25. 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-Blocker 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

  26. Tower of Hanoi: Data & Models Taken from: Anderson, J.R. & Lebiere, C. (1998). The atomic components of thought. Hillsdale, NJ: LEA.

  27. 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.

  28. Chunks & Activation A - F D D I T I O N A C T i s a (p add-numbers =goal> isa add-column num1 =add1 num2 =add2 result nil sum addend1 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 =fact> 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 ) Ai=Bi+SWjSji

  29. 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

  30. P(Ci) Bi = ln () P(Ci) 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

  31. initial expected base-level activation  decay with time, parameter d denotes the decay rate random noise in initial base- level activation 1 at creation time transient noise 2, reflecting moment-to-moment fluctuations Base-Level Activation & Noise Basel-level activation fluctuates and decays with time B(t) =  - d * ln(t) + 1 + 2

  32. 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

  33. P(Ni Cj) P(Ni) 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(Ni|Cj))

  34. -f(Mip + Sp) Timeip = Fe 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

  37. 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-Location 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

  38. Fan Effect

  39. -(A-)/s 1 + e recall is an exponential function of the distance between Activation Ai of Chunk Ci and threshold , scaled by activation noise s. odds of recall decreases as a power function of time Threshold  Chunks with an activation lower than threshold  can notbe retrieved 1 Retrieval probability = (A- )/s Equivalently: Odds of recall = e

  40. 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. ==> Errors of Commission These occur when some wrong chunk is retrieved instead of the correct one and so the wrong instantiation fires. ==>

  41. Partial matching partial matching is restricted to chunks with the sametype as specified in a production’s 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. Negative correlation between knowledge and performance workers 100 200 300 400 500 600 700 800 900 1000 1100 1200 1000 1000 3000 5000 7000 9000 11000 12000 12000 12000 12000 12000 12000 2000 1000 2000 4000 6000 8000 10000 12000 12000 12000 12000 12000 12000 3000 1000 1000 3000 5000 7000 9000 11000 12000 12000 12000 12000 12000 4000 1000 1000 2000 4000 6000 8000 10000 12000 12000 12000 12000 12000 5000 1000 1000 1000 3000 5000 7000 9000 11000 12000 12000 12000 12000 6000 1000 1000 1000 2000 4000 6000 8000 10000 12000 12000 12000 12000 7000 1000 1000 1000 1000 3000 5000 7000 9000 11000 12000 12000 12000 8000 1000 1000 1000 1000 2000 4000 6000 8000 10000 12000 12000 12000 9000 1000 1000 1000 1000 1000 3000 5000 7000 9000 11000 12000 12000 10000 1000 1000 1000 1000 1000 2000 4000 6000 8000 10000 12000 12000 11000 1000 1000 1000 1000 1000 1000 3000 5000 7000 9000 11000 12000 12000 1000 1000 1000 1000 1000 1000 2000 4000 6000 8000 10000 12000 produc t ion sugar 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

  47. Concordance

  48. Transition from computation to retrieval

  49. Goal factoring Success probability Costs expected gain Sequential instantiation No backtracking activation 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

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