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An ACT-R Model of Analogical Mapping

An ACT-R Model of Analogical Mapping. Dario D. Salvucci, John R. Anderson Carnegie Mellon University. Supported in part by a National Science Foundation Graduate Fellowship awarded to Dario Salvucci and Office of Naval Research grant N00014-96-1-0491 awarded to John Anderson.

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An ACT-R Model of Analogical Mapping

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  1. An ACT-R Model of Analogical Mapping Dario D. Salvucci, John R. Anderson Carnegie Mellon University Supported in part by a National Science Foundation Graduate Fellowship awarded to Dario Salvucci and Office of Naval Research grant N00014-96-1-0491 awarded to John Anderson.

  2. big, complex learning mechanisms big defense spending, big hair Life Imitates ACT? ACT & Analogy The World early 80’s late 80’s • mechanisms unite into learning by analogy • Berlin Wall falls, Germany unites early 90’s • analogy mechanism prospers under siege • Clinton prospersunder siege late 90’s • new view of analogy as a production system • new stadiums, new Beetle, new Love Boat !!

  3. The Saga Continues... • Path-mapping theory and model • posits that mapping/analogy… • is a problem-solving skill like any other • is not an architectural primitive • domain: analogical mapping • extends and generalizes description in ACT’98 • Components • representation • path mapping • organization

  4. ss-revolves ss-revolver ss-center revolves revolver planet revolves center sun ss-planet ss-sun Role Representation • Objects and relations • Roles comprising: • parent • parent-type • slot • child-type • child • ACT-R roles: ss-revolver isa role parent ss-revolves parent-type revolves slot revolver child-type planet child ss-planet ss-center isa role parent ss-revolves parent-type revolves slot center child-type sun child ss-sun

  5. Path Mapping • Production system • input: source object, optional source / target roles • output: analogous target object • 8 productions • Features • maps arbitrarily-large structures quickly • allows interplay between role and object/relation similarity • tends to enforce structural consistency

  6. ss-causes at-causes at-revolver ss-effect at-center ss-center at-effect ss-revolver . . . . . . causes effect revolves revolves revolver electron revolves center nucleus revolves revolver planet revolves center sun causes effect revolves ss-revolves at-revolves ss-planet ss-sun at-electron at-nucleus Path Mapping (cont.) Source Target

  7. Path Mapping • Production system • input: source object, optional source / target roles • output: analogous target object • 8 productions • Features • maps arbitrarily-large structures quickly • allows interplay among parent-type, slot, andchild-type • tends to enforce structural consistency

  8. Organization • Describes how a model manages single mappings • Procedural/declarative knowledge specific to task • higher-level analogical skills • maintaining consistent mappings • constraining one-to-one mappings • task-specific and general skills • encoding analogs, generating responses, etc. • Models for two analogical tasks… • use the same representation and productions • may differ greatly in their organizational knowledge • Knowledge included depends on grain size

  9. Illustrative Models • Six illustrative models • path-mapping representation and productions • minimal organizational knowledge • 2 estimated parameter values • Capture many important phenomena, including... • similarity effects (Ross, 1987, 1989) • pragmatic effects (Spellman & Holyoak, 1996) • order effects (Keane et al., 1994) • non-isomorphic mappings (Spellman & Holyoak, 1996) • large analogs (Falkenhainer et al., 1986) • Predict behavior at level of real-world measures • Available from the ACT-R home page

  10. Cond Data Model Ross (1987, 1989) R=.93 +/+ .60 .63 +/– .42 .33 0/+ .54 .60 0/– .39 .38 0/0 .48 .55 Probability-Problem Model

  11. Spellman & Holyoak, 1996 R=.98 Soap-Opera Model

  12. Keane et al., 1994 R=.97 Attribute-Mapping Model

  13. Story-Mapping Model • Task • read 2 storieswith 3 relations • map objects inone story toobjects in theother story • Model • uses path-mapping representation and productions • includes knowledge for encoding, responding, etc. • predicts task time, correctness, gaze durations, gaze transitions, and keystrokes

  14. Conclusions • Path-mapping model... • integrates mapping/analogy with general cognition • predicts low-level behavior for real-world measures • exhibits interesting emergent behavior • Issues • other processes involved in analogy? • similarity and partial matching? • ACT-R and the path-mapping theory • ACT-R constrains theory, helps to explain origins of many common phenomena • theory constrains ACT-R, helps to specify common representations and skills

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