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Understanding Path-Mapping Theory in ACT-R: Analogical Reasoning Insights

This document explores Path-Mapping Theory in ACT-R, adapted and enhanced by Tobias Kaiser. The theory elucidates how analogical reasoning operates by mapping source relations to target relations, exploring object and role relationships within cognitive models. Key concepts include bottom-up and top-down mapping strategies, the significance of central relations, and how existing mappings restrict changes. Through examples including solar system to atom mappings, the document also discusses semantic similarities and various mapping phenomena, highlighting their implications for cognitive psychology and computational modeling.

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Understanding Path-Mapping Theory in ACT-R: Analogical Reasoning Insights

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  1. Introduction • Core Problem of analogical reasoning: Mapping • Source-relation → Target-relation • Source-object → Target-object • Salvucci & Anderson: Path-mapping • Rolles link objects, relations and higher order relations together. • Source-role → Target-role Path-Mapping Theory in ACT-R Tobias Kaiser

  2. Example: Solar System ↔ Atom causes[attracts(sun, planet), revolves(planet, sun)] Path-Mapping Theory in ACT-R Tobias Kaiser

  3. To map an object... • Determine a path from the object to the root relation (bottom-up) • Map the root relation • Map the roles underneath (top-down) • Existing mappings are not allowed to be changed! Path-Mapping Theory in ACT-R Tobias Kaiser

  4. Mapping-Phänomene • Spellman & Holoyak: Multiple possible mappings, central relations are dominant (Soap-Opera Model) • Nonisomorphic Mappings, many-to-one mappings are dominant (Country-Mapping Model) • Relations arity can be mapped to a different arity. (Sharing-Model) • B. Ross: Semantic and structural similarity ease the mapping process (Probability Problem Model) • Keane et al.: ''Unnatural'' analogies lead to a longer reaction time (Attribute-Mapping Model) Path-Mapping Theory in ACT-R Tobias Kaiser

  5. Story mapping task • One-Story Condition: Subjects saw only the target story during mapping phase • Two-Story Condition: Subjects saw both stories Path-Mapping Theory in ACT-R Tobias Kaiser

  6. Performance, reaction time, gazes Path-Mapping Theory in ACT-R Tobias Kaiser

  7. Gaze transitions Path-Mapping Theory in ACT-R Tobias Kaiser

  8. Story mapping model Chunk-definition for Roles: (chunk-type role parent parent-type slot child child-type) Example: rested-on(Larry, couch) (s1-1 isa target-role parent rested-on-1 parent-type rested-on slot rested-on-agent child larry child-type person) Goal Stack: Map an object (chunk-type map-object source-object source-role target-role target-object void source-relation target-relation parent-type slot child-type) Path-Mapping Theory in ACT-R Tobias Kaiser

  9. Walking up the path... (p Retrieve-Components =goal> isa map-object source-role =source-role source-relation nil parent-type nil slot nil child-type nil =source-role> isa source-role parent =source-relation parent-type =parent-type slot =slot child-type =child-type ==> =goal> source-relation =source- relation parent-type =parent-type slot =slot child-type =child-type) (p Retrieve-Source-Role =goal> isa map-object source-object =source-object source-role nil target-object nil =source-role> isa source-role child =source-object ==> =goal> source-role =source-role) If no Source-Role is found: Reached-Source-Path-Root Path-Mapping Theory in ACT-R Tobias Kaiser

  10. ...and down again! (p Retrieve-Analog-At-Root =goal> [...] parent-type =parent-type slot =slot child-type =child-type target-role nil =target-role> parent =target-relation parent-type =parent-type slot =slot child-type =child-type child =target-object ==> =subgoal> target-object =target-relation =goal> target-object =target-object !focus-on! =subgoal) (p Map-Source-Relation =goal> isa map-object source-relation =source-relation target-relation nil ==> =subgoal> isa map-object source-object =source-relation target-object =target-relation =goal> target-relation =target-relation !push! =subgoal) Path-Mapping Theory in ACT-R Tobias Kaiser

  11. Semantic similarity (my-set-similarities-story '((got obtained) (unpacked took-out) (planned chose) (prepared set) (walked-to drove-to) (paid-for bought) (carried brought) (placed planted) (cleaned cleared) (prepared readied)(gathered collected) (slept-on rested- on) (fell-to ran-into) (broke sprained) (phoned called) (completed finished) (slept-on rested-on) (played toyed- with) (stole grabbed) (broke crushed) (whined-to cried- to) (purchased bought) (prepared organized) (talked-to spoke-with) (lifted picked-up) (pulled tugged) (ran- on walked-on) (started began) (added-to put-on) (finished completed) (dodged avoided) (tossed threw) (ran-on jogged-on) (arranged prepared) (collected gathered) (spoke-to talked- to) (gathered collected) (set-up put-up) (typed-in wrote-in) (sawed bowed) (blew-on whistled) (hammered beat) (monitored watched) (gripped held) (extracted removed) (gathered collected) (assembled built) (painted stained)) *estimated-similar-match*) Path-Mapping Theory in ACT-R Tobias Kaiser

  12. Parameters (defparameter *data-story* (make-data-story :correct '(.85 .73 .99 .94) :times '((14.4 14.4 6.7 6.6) (12.9 18.3 12.2 14.5)) :gazes '((4.5 6.3 3.8) (2.4 2.5 1.5) (3.1 6.2 4.6) (2.6 4.1 2.4 2.7 3.9 2.9)) :transitions '(#2a((0 .92 .08) (.41 0 .59) (.18 .82 0)) #2a((0 .89 .11) (.30 0 .70) (.15 .85 0)) #2a((0 .39 .10 .22 .21 .09) (.26 0 .27 .04 .27 .16) (.06 .33 0 .05 .21 .35) (.33 .25 .05 0 .33 .04) (.08 .41 .10 .14 0 .26) (.07 .23 .29 .08 .33 0))) :key-times '((.51 .80 .90) (.52 .79 .92)) :key-before-23 '(.18 .07))) Path-Mapping Theory in ACT-R Tobias Kaiser

  13. Parameters (defparameter *data-story* (make-data-story :correct '(.85 .73 .99 .94) :times '((14.4 14.4 6.7 6.6) (12.9 18.3 12.2 14.5)) :gazes '((4.5 6.3 3.8) (2.4 2.5 1.5) (3.1 6.2 4.6) (2.6 4.1 2.4 2.7 3.9 2.9)) :transitions '(#2a((0 .92 .08) (.41 0 .59) (.18 .82 0)) #2a((0 .89 .11) (.30 0 .70) (.15 .85 0)) #2a((0 .39 .10 .22 .21 .09) (.26 0 .27 .04 .27 .16) (.06 .33 0 .05 .21 .35) (.33 .25 .05 0 .33 .04) (.08 .41 .10 .14 0 .26) (.07 .23 .29 .08 .33 0))) :key-times '((.51 .80 .90) (.52 .79 .92)) :key-before-23 '(.18 .07))) Path-Mapping Theory in ACT-R Tobias Kaiser

  14. Summary • Model Performance, RT and eye movements are similar to human behavior • Possibly due to parameters • Many cognitive tasks are not addressed in the model: • Reading/internalizing the story • Extracting Objects and Relations • Semantic comparison Path-Mapping Theory in ACT-R Tobias Kaiser

  15. Summary • Structure of the Story mapping task is too simple • Every relation has two arguments. One is a person, the other one not adressed in the model • No higher order relations • The model does not show the real strength of path mapping! Path-Mapping Theory in ACT-R Tobias Kaiser

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