1. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.1 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. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.2 Life Imitates ACT? big, complex learning mechanismsbig, complex learning mechanisms big defense spending, big hairbig defense spending, big hair early 80’s ACT & Analogy The World mechanisms unite into learning by analogymechanisms unite into learning by analogy analogy mechanism prospers under siegeanalogy mechanism prospers under siege new view of analogy as a production systemnew view of analogy as a production system Berlin Wall falls, Germany unitesBerlin Wall falls, Germany unites Clinton prospers under siegeClinton prospers under siege new stadiums, new Beetle, new Love Boat !!new stadiums, new Beetle, new Love Boat !! late 80’s early 90’s late 90’s

3. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.3 Path-mapping theory and modelPath-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 ComponentsComponents –representation –path mapping –organization The Saga Continues...

4. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.4 Role Representation Objects and relationsObjects and relations Roles comprising:Roles comprising: –parent –parent-type –slot –child-type –child ACT-R roles:ACT-R roles: ss-revolves ss-revolver revolvesrevolverplanet ss-planet ss-center revolvescentersun ss-sun ss-revolver isa role parentss-revolves parent-typerevolves slotrevolver child-typeplanet childss-planet ss-center isa role parentss-revolves parent-typerevolves slotcenter child-typesun childss-sun

5. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.5 Path Mapping Production systemProduction system –input: source object, optional source / target roles –output: analogous target object –8 productions FeaturesFeatures –maps arbitrarily-large structures quickly –allows interplay between role and object/relation similarity –tends to enforce structural consistency

6. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.6 Path Mapping (cont.) Source at-revolves at-revolver revolvesrevolverelectron at-electron at-center revolvescenternucleus at-nucleus at-causes at-effect causeseffectrevolves... Target ss-revolves ss-planet ss-center revolvescentersun ss-sun ss-causes ss-effect causeseffectrevolves... ss-revolver revolvesrevolverplanet

7. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.7 Path Mapping Production systemProduction system –input: source object, optional source / target roles –output: analogous target object –8 productions FeaturesFeatures –maps arbitrarily-large structures quickly –allows interplay among parent-type, slot, and child-type –tends to enforce structural consistency

8. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.8 Organization Describes how a model manages single mappingsDescribes how a model manages single mappings Procedural/declarative knowledge specific to taskProcedural/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…Models for two analogical tasks… –use the same representation and productions –may differ greatly in their organizational knowledge Knowledge included depends on grain sizeKnowledge included depends on grain size

9. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.9 Illustrative Models Six illustrative modelsSix illustrative models –path-mapping representation and productions –minimal organizational knowledge –2 estimated parameter values Capture many important phenomena, including...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 measuresPredict behavior at level of real-world measures Available from the ACT-R home pageAvailable from the ACT-R home page

10. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.10 +/+.60.63 +/–.42.33 0/+.54.60 0/–.39.38 0/0.48.55 CondDataModel Ross (1987, 1989) R=.93 Probability-Problem Model

11. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.11 Soap-Opera Model Spellman & Holyoak, 1996 R=.98

12. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.12 Attribute-Mapping Model Keane et al., 1994 R=.97

13. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.13 Story-Mapping Model TaskTask –read 2 stories with 3 relations –map objects in one story to objects in the other story ModelModel –uses path-mapping representation and productions –includes knowledge for encoding, responding, etc. –predicts task time, correctness, gaze durations, gaze transitions, and keystrokes

14. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999.14 Conclusions Path-mapping model...Path-mapping model... –integrates mapping/analogy with general cognition –predicts low-level behavior for real-world measures –exhibits interesting emergent behavior IssuesIssues –other processes involved in analogy? –similarity and partial matching? ACT-R and the path-mapping theoryACT-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