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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 N00014-961-0491 awarded to John Anderson. Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 1 Life Imitates ACT? ACT & Analogy The World early 80’s • big, complex learning mechanisms • big defense spending, big hair late 80’s • mechanisms unite into learning by analogy • Berlin Wall falls, Germany unites early 90’s • analogy mechanism prospers under siege • Clinton prospers under siege late 90’s • new view of analogy as a production system • new stadiums, new Beetle, new Love Boat !! Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 2 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 Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 3 Role Representation • Objects and relations • Roles comprising: – parent – parent-type – slot – child-type – child ss-revolves ss-revolver revolves revolver planet ss-center revolves center sun ss-planet ss-sun • ACT-R roles: ss-revolver isa role parent parent-type slot child-type child ss-revolves revolves revolver planet ss-planet Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. ss-center isa role parent parent-type slot child-type child ss-revolves revolves center sun ss-sun 4 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 Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 5 Path Mapping (cont.) Source Target ss-causes at-causes ss-effect causes effect revolves . . . . . . ss-revolves at-effect causes effect revolves at-revolves ss-revolver revolves revolver planet ss-center revolves center sun at-revolver revolves revolver electron at-center revolves center nucleus ss-planet ss-sun at-electron at-nucleus Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 6 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, and child-type – tends to enforce structural consistency Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 7 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 Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 8 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 Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 9 Probability-Problem Model Ross (1987, 1989) R=.93 Cond Data Model +/+ .60 .63 +/– .42 .33 0/+ .54 .60 0/– .39 .38 0/0 .48 .55 Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 10 Soap-Opera Model Spellman & Holyoak, 1996 Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. R=.98 11 Attribute-Mapping Model Keane et al., 1994 Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. R=.97 12 Story-Mapping Model • Task – read 2 stories with 3 relations – map objects in one story to objects in the other story • Model – uses path-mapping representation and productions – includes knowledge for encoding, responding, etc. – predicts task time, correctness, gaze durations, gaze transitions, and keystrokes Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 13 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 Dario Salvucci, Carnegie Mellon University. ACT-R Workshop, August 6-9, 1999. 14