1. Functional encoding in memory for goals ACT-R workshop August 1999 Erik M. Altmann (altmann@gmu.edu) J. Gregory Trafton (trafton@itd.nrl.navy.mil)

2. Means-ends tasks Means-ends behavior: –Suspend a goal –Work on subgoals –Resume the goal at an appropriate time Examples: –Monkey and bananas –Giving a talk –Making photocopies

3. The Tower of Hanoi The foundational means-ends task –In cognitive science Understood in terms of the goal stack Completely understood –Or is it? Good data (Anderson, Kushmerick, & Lebiere, 1993)

4. The Tower of Hanoi 4 CAB 3 2 1 4 Goal 4:CSubgoal 3:B 3

5. A stack model 4:C 3:B 4:C 2:C 3:B 4:C 1:B 2:C 3:B 4:C 2:C 3:B 4:C 3:B 4:C 1:C 3:B 4:C... Time Stack height Push 3:B Recall 3:B perfectly, despite lag

6. The stack as representation The typical assumption in task analysis –Implicit in problem behavior graph –Explicit in GPS, GOMS,... The standard theory of goal management –In cognitive architectures ACT-R, Soar –In cognitive models generally E.g., ACT-PRO, 3CAPS Better Raven,...

7. The stack as representation The appeal: –Robust and general –Applies to a wide variety of tasks –Supported by empirical data At some level of abstraction The problem: –At best, a high-level simplification –At worst, wrong

8. Goal-selection order LIFO order not used when not needed –Selection order in arithmetic (VanLehn) Order depends on context –Display-based problem-solving, situated action, distributed representation –Capture error

9. Pending goals Displaced by memory load (Just & Carpenter) Decay when not rehearsed (Byrne & Bovair) Intrude when rehearsed (Altmann & Trafton, 1999b) Affected by goal content –Intention superiority (Goschke & Kuhl) Suggesting that activation affects availability

10. Research approach Model Tower of Hanoi data without a stack –For goals Ask how to make up the lost functionality –Domain knowledge –External cues –Existing memory theory If it suffices, the theory is strengthened If it fails, then at least we know why

11. Memory as goal store (MAGS) Memory = encoding + retention + retrieval Assume passive retention Assume strategic encoding –Using knowledge of retrieval context Assume strategic retrieval –Using knowledge to select retrieval cues

12. Analytical framework: Activation What happens to a goal’s activation over time? Two kinds of activation (in ACT-R): –Base-level activation from use –Priming from context Total activation predicts current need –So memory returns the most active element

13. Encoding to resist decay Strengthen base-level activation Strength test to say how much is enough –Cognition asking itself, “Got it?” If yes, stop strengthening and move on If no, strengthen some more –Test interleaved with strengthening Strengthen enough but not too much

14. Encoding to resist decay Retrieval threshold Strength test Base-level activation Time 2:C, 1:B, 2:C

15. The strength test Cognition can anticipate retrieval context –Retrieval cue — “3” for 3:B –Retention interval — 5 to 10 seconds Anticipations are just knowledge –Represent as cue chunks Test-retrieve the goal –If test fails, encode some more

16. Focussed retrieval 3:B Test retrieval cue: 3 sink:S Retrieval disk: 3 from: A to: B blocked: t Encoding context Retrieval context disk: 3 from: A to: B blocked: t Main focus cue: 3 Retrieval focus Goal

17. Retrieval production (p retrieve =focus> isa retrieval =goal> isa goal disk =disk to =peg ==> =focus> disk =disk to =peg !pop!) Noisy retrieval without partial matching No indexing or chaining

18. Empirical test Anderson, Kushmerick, & Lebiere (1993) –Subjects instructed in goal-recursion strategy –Response-time data are from perfect trials Cognition on those trials most stack-like Strongest test of the MAGS model

19. Prediction Encoding a goal is expensive –Not a cost-free push operation –A second or so per goal Prediction from serial attention model

20. Data Large peaks = Goal encoding Time (sec)

21. Prediction People avoid unnecessary retrievals –Retrieval is effortful and error-prone Use move heuristics when they apply: Don’t-undo IFthe just-moved disk was 1, and X is the smaller of the two other top disks, and Y is the larger of the two other top disks, THENmove X on top of Y.

22. Data Valleys = Don’t-undo

23. Prediction Prefer goal retrieval to re-planning Depends on selecting the right retrieval cue –No perfect pop operation Cue selection heuristic: Retrieve-uncovered IFthe uncovered disk is X, THENtry to retrieve X:?

24. Data Small peaks = goal retrieval

25. Five-disk data

26. Parameters ACT-R defaults: –W = 1.0, F = 1.0, d = 0.5 Adopted from other models: –Perceptual encoding time = 185 msec (Anderson, Matessa, & Lebiere, 1997) –  = 4.0, s = 0.3 (Altmann & Gray) No unconstrained parameters

27. Prediction Retrieval is error prone –E.g., might retrieve 3:C instead of 3:B From a previous plan or previous trial –Incorrect retrieval starts a garden path

28. Data Length of solution path Optimal

29. MAGS vs. stack model (A&L 98) Based on declarative memory –Not on a privileged stack Broader empirical coverage –Detailed account of RT and error –Only ToH model to address both (before today) Functional encoding and retrieval processes –Specified at ACT-R’s atomic level –Generic — adapted from serial attention (Altmann & Gray, 1999b)

30. Implications Need a two-high architectural stack –A main focus for problem state –A retrieval focus for concentrating Main and retrieval focuses are mutually exclusive (Altmann & Trafton, 1999b) –One is reliable –One is predictive

31. Conclusions Don’t need a goal stack –Anything it can do, MAGS can do better –And without that much more analysis Don’t want a goal stack –Too easy and too wrong –Masks real goal-management mechanisms

32. Conclusions 40 years of research on the Tower of Hanoi Yet retrieve-uncovered is unpublished –Missing from Simon’s perceptual strategies –Missing from Anzai and Simon protocol

33. Conclusions Why now? –Detailed data –A precise memory theory –Throwing away the goal stack

34. References Model code : hfac.gmu.edu/people/altmann/toh Altmann & Trafton (1999a). Memory for goals: An architectural perspective. Proc. Cog. Sci. 21. Altmann & Trafton (1999b). Memory for goals in means-ends behavior. Manuscript submitted for publication.

35. The encoding process disk: 4 from: A to: C blocked: t disk: 4 from: A to: C blocked: t Test-passes/fails 4:C Test-retrieval Focussed retrieval with a “sink” cue: 4 sink:S disk: 4 from: A to: C blocked: t Test-strength Test-fails Strengthen-goal