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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.

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## Introduction

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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

Example: Solar System ↔ Atom

causes[attracts(sun, planet), revolves(planet, sun)]

Path-Mapping Theory in ACT-R

Tobias Kaiser

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

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

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

Performance, reaction time, gazes

Path-Mapping Theory in ACT-R

Tobias Kaiser

Gaze transitions

Path-Mapping Theory in ACT-R

Tobias Kaiser

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

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

...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

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

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

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

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

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