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CogSketch - Qualitative reasoning group
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1. 50 of glyph1 participates in the occlusion 2 glyph1 occludes more than 50 of glyph2 from glyph3 or 3 glyph1 occludes more than 50 of glyph3 from glyph 2 5 2 ABOUT THE OBJECTS REPRESENTED BY THE GLYPHS 5 2 1 PHYSICAL VIEW GENRE LOOKING FROM SIDE POSE above obj1 obj2 Can be generated on demand by fire ask Says that obj1 is above obj2 below obj1 obj2 Can be generated on demand by fire ask Says that obj1 is above obj2 Note that above is our canonical representation Calling nusketch compute positional relations where some object A is below of some other object B will not generate a below fact but will instead generate above B A rightOf obj1 obj2 Can be generated on demand by fire ask Says that obj1 is to the right of obj2 leftOf obj1 obj2 Can be generated on demand by fire ask Says that obj1 is to the left of obj2 Note that rightOf is our canonical representation Calling nusketch compute positional relations where some object A is left of some other object B will not generate a leftOf fact but will instead generate rightOf B A positionalRelationFor obj1 obj2 rel Can be generated on demand by fire ask Says that the given positional relation holds between the two objects enclosesVertically obj1 obj2 Can be generated on demand by fire ask Says that obj2 is completely within the vertical bounds determined by the minimum Y coordinate and maximum Y coordinate of obj1 enclosesHorizontally obj
2. aspect ratio Other shape with multiple axes of symmetry Shape with no detected symmetry axes but with no axes of elongation suggesting an overall regular shape Shape whose edges are aligned with x and y axes Shape whose edges are diagonal non axis aligned Tiny closed shape based on distribution of sizes in a context ao Element located at the center of an image Element located at the left top side of an image Describes shapes whose edges are narrow or wide relative to other shapes in the context Shape with fill color X Shape with edges of color X Object with some fill texture a set of parallel straight lines inside it A These attributes describing shape or location are important in guiding the comparison between images However when Spatial Routines represent the pattern of variance between images they are abstracted out They are replaced with changes in spatial relations and with shape transformations see below S These attributes describe rotation invariant features of an object s shape 9 2 SPATIAL RELATIONS These are the relations used by spatial routines 17 Type Relative position Topology Frame of reference relations Alignment relations Transformation relations Term above X Y rightOf X Y elementContains X Y elementsIntersect X Y elementsOverlap X Y 5 centeredOn X Y onLeft Right Top BottomHalfOf X Y parallelElements X Y 5 perpen
3. glyph2 Can be generated on demand by fire ask Says the same thing as objectContains except that transitive containment is preserved l e if glyph1 contains glyph2 and glyph2 contains glyph3 then objectContains Transitive glyph1 glyph3 will hold whereas objectContains glyph1 glyph3 will not 4 VORONO DIAGRAM RELATIONS The following facts are derived from the voronoi diagrams computed for a subsketch Note that more than one voronoi may be computed for a given subsketch rules in our knowledge base which voronoi diagrams get computed For example in nuSketch Battlespace voronoi diagrams are made for the terrain information pathways avenues of approach etc and the enemy and friendly military units In CogSketch we currently just compute one voronoi diagram for each subsketch using all the glyphs on the subsketch as input vAdjacent glyph1 glyph2 Can be generated on demand by fire ask Says that the two glyphs are adjacent to each other on at least one of the voronoi diagrams containing both glyphs The two glyphs are considered adjacent if at least one voronoi site cell of glyph1 is touching a site of glyph2 vNear glyph1 glyph2 Can be generated on demand by fire ask Says that the two glyphs are near each other on at least one of the voronoi diagrams containing both glyphs The notion of near is a bit looser than that of adjacent To compute a region of nearness around a glyph we include all the immediately ad
4. object in real world units i e if the glyph is a square that is one unit wide by one unit tall and each unit represents 10 Km then the area would be Kilometer 100 The area is computed using the blob boundary of the glyph that represents the specified object centralReferencePoint object point Can be generated on demand by fire ask Specifies the centroid of the object in real world units The centroid is computed from blob boundary of the glyph that represents the specified object distanceBetween obj1 obj2 distance Can be generated on demand by fire ask Returns the distance between the glyphs representing the two objects entityCentroidOnPath obj path glyph Can be generated on demand by fire ask entityCentroidOnPath probe path is true exactly when probe is close enough to some point on path as determined by path s width entityLocatedAt obj location obj Can be generated on demand by fire ask Object is located at location meaning inside or overlapping or touching entityLocatedInside obj location obj Can be generated on demand by fire ask Object is located inside location facingRelation obj1 obj2 facingRelationSpecifier Can be generated on demand by fire ask Says that the specified relation holds between the facing directions of Obj1 and Obj2 Acceptable relations here are onLeftFlank Facing onRightFlank Facing onRear Facing and onFront Facing fixedAxisRotation situation1 situation2 obj1 o
5. 1 obj2 Can be generated on demand by fire ask Says that obj2 is completely within the horizontal bounds determined by the minimum X coordinate and maximum X coordinate of obj1 5 2 2 PHYSICAL VIEW GENRE LOOKING FROM TOP POSE positionalRelationFor obj1 obj2 rel Can be generated on demand by fire ask Says that the given positional relation holds between the two objects 5 2 3 PHYSICAL VIEW GENRE LOOKING FROM BOTTOM POSE positionalRelationFor obj1 obj2 rel Can be generated on demand by fire ask Says that the given positional relation holds between the two objects 5 2 4 GEOSPATIAL VIEW GENRE LOOKING FROM TOP POSE eastOf obj1 obj2 Can be generated on demand by fire ask northEastOf obj1 obj2 Can be generated on demand by fire ask northOf obj1 obj2 Can be generated on demand by fire ask northWestOf obj1 obj2 Can be generated on demand by fire ask westOf obj1 obj2 Can be generated on demand by fire ask southOf obj1 obj2 Can be generated on demand by fire ask southWestOf obj1 obj2 Can be generated on demand by fire ask southEastOf obj1 obj2 Can be generated on demand by fire ask positionalRelationFor obj1 obj2 rel Can be generated on demand by fire ask Says that the given positional relation holds between the two objects compassPositionalRelationFor obj1 obj2 rel Can be generated on demand by fire ask rel will be one of eastOf northEastOf northOf northWestOf westOf southWe
6. CogSketch Spatial Reasoning Madeline Usher Ken Forbus Andrew Lovett Matthew McLure VERSION OF 6 27 2012 CONTENTS 1 1 1 1 2 5 1 5 2 6 6 1 6 2 7 8 9 9 1 9 2 9 3 9 4 INTRODUCTION ACCESSING SPATIAL REASONING FACILITIES BRIEF OVERVIEW OF REPRESENTATION AND REASONING IN COGSKETCH RCC 8 RELATIONS HIGHER LEVEL TOPOLOGICAL RELATIONS VORONO DIAGRAM RELATIONS POSITIONAL RELATIONS ABOUT THE GLYPHS ABOUT THE OBJECTS REPRESENTED BY THE GLYPHS GLYPH GROUPS CONTAINMENT CONNECTNESS MISCELLANEOUS GEOMETRY VISUAL CONCEPTUAL RELATIONS RELATIONS USED IN SPATIAL ROUTINES OBJECT ATTRIBUTES SPATIAL RELATIONS PATTERN OF VARIANCE RELATIONS SPATIAL TRANSFORMATION ATTRIBUTES 12 12 12 13 15 16 16 17 19 19 1 INTRODUCTION This is a very preliminary draft of documentation describing the spatial reasoning facilities built into CogSketch We are making this draft documentation available to support those who wish to experiment with these facilities as they evolve 1 1 ACCESSING SPATIAL REASONING FACILITIES If you just want to try things out a good way to get started is to use the Query window available through the knowledge inspector or by selecting the View Query Window menu option You ll find the concordance of objects to names in the left hand frame useful for formulating queries These facilities are also available through the KQML server via the ASK operation 1 2 BRIEF OVERVI
7. EW OF REPRESENTATION AND REASONING IN COGSKETCH Mostly yet to be written Here are the absolutely key points 1 2 1 STRUCTURE OF SKETCHES Internally each subsketch corresponds to a reasoning context i e a microtheory In our knowledge representations we use ist Information lt subsketch context gt lt fact gt 1 2 2 TRUTH MAINTENANCE CONSIDERATIONS All results are cached in the LTRE that serves as FIRE s working memory so that they can be used in explanations cf the drill down in the knowledge inspector This also enables results to be appropriately retracted when the sketch is changed This is why spatial conclusions tend to include statements about the time the ink of the glyphs involved were last updated Whenever a glyph is moved the now obsolete last ink assumption is retracted and a new assumption made This updating is part of what is happening when ink processor displayed as the left eye in the interface is operating 2 RCC 8 RELATIONS The RCC 8 relations are a set of eight mutually exclusive relations that describe all possible topological relations between two 2D closed shapes Do Ce CF RCC8 DC RCC8 EC RCC8 PO RCC8 EQ RCC8 TPP RCC8 NTPP RCC8 TPPi RCC8 NTPPi rcc8 DC glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Can be generated on demand by fire ask disconnected rcc8 EC glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Can be generated on de
8. derived from both kinds of information For example two glyphs that touch could indicate that they are rigidly connected hinged or any of a number of other possibilities depending on the specific kinds of entities involved To specify these relationships for a sketch click on the 2 icon A browser window will open providing a form which enables you to choose a specific relationship for each pair of entities that have a form of visual relationship When you are finished selecting relationships click the submit button If you need to change any of the VCR relationships check the retract box underneath that relationship and click the submit button You should get the drop down menu again and you can re assign the relationship between the involved glyphs Some things to know about this computation e The set of possible candidates can be quite large or quite small depending on the visual and conceptual properties of the entities involved Having over one hundred possibilities is not uncommon Sorting through them can be complex and we recommend having a KB Browser window open on the side while you are familiarizing yourself with the options e Only relations whose argument type constraints are consistent with the declared types of the entities are presented as possibilities No other information is currently used to filter the set e g it does not try to derive each of the possibilities and its negation using the information in the sketch plus
9. dicularElements X Y gt collinearElements X Y gt centeredOn X Y reflectedShapes XAxis X Y reflectedShapes YAxis X Y gt reflectedShapes X Y rotatedShapes 90 X Y rotatedShapes 180 X Y gt rotatedShapes X Y Description Object X is above object Y Object X is right of object Y Closed shape X contains object Y The edges of objects X and Y intersect The interiors of closed shapes X and Y overlap Object X contains object Y Object X creates a frame of reference in which object Y s relative location can be encoded In this case object Y is located at the center of object X ao X and Y are single edges are rows of objects They are parallel a X and Y are single edges and are collinear or X is a single edge and Y is a small object that lies along its extension This relation can also indicate X is a single edge or set of edges and Y lies at its center Indicates that there is a reflection between the two objects shapes Indicates that there is some other reflection Indicates there is a rotation between the two objects shapes Indicates that there is some other rotation S Symmetric relations in which the order of the arguments is irrelevant E g elementsOverlap X Y gt elementsOverlap Y X 18 9 3 PATTERN OF VARIANCE RELATIONS When a Spatial routine computes a pattern of variance between images it compares the images visual representations containi
10. e that s been reflected over one of the two diagonal 45 degree axes A shape that s been reflected over some other axis A shape that s become bigger A shape that s become smaller A shape that s become longer along one dimension One part of a shape has become longer A shape that s had a part added to it A shape that s become shorter along one dimension One part of a shape has become shorter A shape that s had a part removed from it A shape that s been added A shape that s been removed A shape that s remained unchanged NOTE If a shape remains constant throughout the images being compared it is not represented at all in the pattern of variance On the other hand if a shape remains constant between two images and then transforms in a third image then its remaining constant between the first two images will be represented using ConstantShape 20
11. econd argument relativePositionAlong Path Spatial SpatialThing Localized SpatialThing Localized PathRelativePositionRelation Can be generated on demand by fire ask relativePositionAlong path probe ref relation states that relation holds for probe relative to ref along path relativePositionChange situation1 situation2 obj1 obj2 qualitative vector Can be generated on demand by fire ask Gives the qualitative change in the vector difference between obj2 and obj1 that happened between situation1 and situation2 shortestRotationDir situation1 situation2 obj rotation dir Can be generated on demand by fire ask Indicates the direction in which obj rotated between situation1 and situation2 surfaceOverlapDirToPoint QMSurface QMSurface QMPoint QualitativeVector Can be generated on demand by fire ask surfaceOverlapDirToPoint is true iff the qvector is the direction from the midpoint of the overlap of the two surfaces to the qpoint ConvexHullFn glyph A functional wrapper that can be wrapped around any glyph when querying for a topological relationship The query will effectively replace the glyph in the query with its convex hull 14 8 VISUAL CONCEPTUAL RELATIONS For many reasoning tasks it is helpful to clarify for CogSketch what relationship holds between the objects depicted based on the visual relationships that hold between the glyphs that depict them We call these visual conceptual relationships since they are
12. eric Implicit Shape Proximal Similar Shape Group Dot Shape VerticalEdge HorizontalEdge S 2D Shape Closed gt 2D Shape Open gt 2D Shape Convex gt Description Any visible 2D shape A shape implied by negative space A group formed of several similar closed shapes that are about equally distant from each other Special shape dot any very small glyph Shape consisting of a single straight edge horizontally or vertically aligned Any closed shape Any open shape Closed shape without any concavities 16 Curvedness Junctions Symmetry Alignment Relative Size Relative Location Relative Edge Width Fill Color Edge Color Texture 2D Shape Curved gt 2D Shape Straight gt 2D Shape Forked gt Symmetric Shape gt Perpendicular Symmetric Shape gt Fully Symmetric Shape gt Multipley Symmetric Shape gt Symmetric Blob 2D Shape AxisAligned 2D Shape Oblique TinySizeGyph Small Medium LargeSizeGlyph Centered Element OnLeft Element OnTop Element narrowEdged wideEdged ObjectsColoredFn X ObjectsBorder ColoredFn X TexturedObject Shape with only curved edges Shape with only straight edges Shape with junctions where 3 edges meet Shape with one axis of symmetry Shape with two perpendicular axes of symmetry Shape with two perpendicular axes of symmetry plus at least one more axis and with a fairly even
13. ider inside glyph glyph group Automatically computed between glyphs on a subsketch Says that inside glyph is one of the glyphs contained inside in the specified ContainedGlyphGroup and is touching the interior wall of the containing glyph containedGlyphGroupContainer outside glyph glyph group Automatically computed between glyphs on a subsketch Says that outside glyph is the glyph containing the inside glyphs in the specified ContainedGlyphGroup 6 2 CONNECTNESS isa ConnectedGlyphGroupFn TheList glyph1 glyph2 ConnectedGlyphGroup Automatically computed between glyphs on a subsketch Reifies a group of connected glyphs connectedGlyphGroupMember glyph glyph group Automatically computed between glyphs on a subsketch Says that glyph is one of the glyphs contained inside in the specified ConnectedGlyphGroup connectedGlyphGroupTangentialConnection glyph1 glyph2 glyph group Automatically computed between glyphs on a subsketch Says that glyph1 and glyph2 are connected because their outsides are touching and that they belong to the specified ConnectedGlyphGroup glyphGraphEdgesFor glyph graph glyph TheList connected glyph1 connected glyph2 Automatically computed between glyphs on a subsketch Says that glyph is a node in glyph graph whose arcs consist of links to the glyphs in the given list 12 7 MISCELLANEOUS GEOMETRY areaOfObject object area Can be generated on demand by fire ask Gives the area of the
14. jacent sites and expand outwards into sites whose area is mostly encompased by the adjacent sites vBetweenglyph1 glyph2 glyph3 Can be generated on demand by fire ask Says that glyph2 is between glyph1 and glyph3 on at least one of the voronoi diagrams containing both glyphs 5 POSITIONAL RELATIONS 5 1 ABOUT THE GLYPHS above glyph1 glyph2 Can be generated on demand by fire ask Says that glyph1 is above glyph2 in the sketch coordinate system Y values increase as you go upwards higher values are above lower values below glyph1 glyph2 Can be generated on demand by fire ask Says that glyph1 is below glyph2 in the sketch coordinate system Y values increase as you go upwards higher values are above lower values Note that above is our canonical representation Calling nusketch compute positional relations where some glyph A is below of some other glyph B will not generate a below fact but will instead generate above B A rightOf glyph1 glyph2 Can be generated on demand by fire ask Says that glyph1 is to the right of glyph2 in the sketch coordinate system X values increase as you go towards the right leftOf glyph1 glyph2 Can be generated on demand by fire ask Says that glyph1 is to the left of glyph2 in the sketch coordinate system X values increase as you go towards the right Note that rightOf is our canonical representation Calling nusketch compute positional relations where some glyph A is left of s
15. mand by fire ask edge connected rcc8 PO glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Can be generated on demand by fire ask partial overlap rcc8 EQ glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Can be generated on demand by fire ask equal rcc8 TPP glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Can be generated on demand by fire ask tangential proper part 1 Cohn A Calculi for qualitative spatial reasoning In Artificial Intelligence and Symbolic Mathematical Computation LNCS 1138 eds J Calmet J A Campbell J Pfalzgraph Springer Verlag 1996 124 143 rcc8 TPPi glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Can be generated on demand by fire ask inverse tangential proper part rcc8 NTPP glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Can be generated on demand by fire ask non tangential proper part rcc8 NTPPi glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Can be generated on demand by fire ask inverse non tangential proper part hasRCC8Relation glyph1 glyph2 rel Automatically computed between pairs of glyphs on same layer Can be generated on demand by fire ask Says that the given RCC8 relation holds for the two glyphs 3 HIGHER LEVEL TOPOLOGICAL RELATIONS CogSketch can compute several higher level topological relation
16. ng the attributes and relations described above It produces a set of relations describing changes between the images These relations are given below Term Description changeBetweenImages fact Image X Image Y Indicates that a fact holds in Image Y but not in Image X Indicates that a relation reverses between Images X and Y For example Object A may be above Object B in Image X but below Object B in Image Y reversalBetweenImages fact X fact Y Image X Image Y Indicates an object transformation between Images X and Y For example an object might rotate or it might change shape entirely See the next table for a list of possible transformations changeBetweenImagesFromTo fact X fact Y Image X Image Y Indicates a that fact holds in Image X This relation may be used holdsinimage fact ImegeX instead of changeBetweenlmages in special cases 9 4 SPATIAL TRANSFORMATION ATTRIBUTES When a spatial routine computes a pattern of variance between images it represents changes to an object s shape with the relation changeBetweenlmagesFromTo isa Element 1 Spatial trans attribute isa Element 1 Spatial trans attribute Image X Image Y The attributes may describe a transformation such as a rotation a deformation such as becoming longer or a total change in shape A generalized form allows the Structure Mapping Engine our model of comparison to generalize when comparing representations For example it may be possible
17. ome other glyph B will not generate a leftOf fact but will instead generate rightOf B A positionalRelationFor glyph1 glyph2 rel Can be generated on demand by fire ask Says that the given positional relation holds between the two glyphs For glyphs rel will be one of above below rightOf or leftOf enclosesVertically glyph1 glyph2 Can be generated on demand by fire ask Says that glyph2 is completely within the vertical bounds determined by the minimum Y coordinate and maximum Y coordinate of glyph1 enclosesHorizontally glyph1 glyph2 Can be generated on demand by fire ask Says that glyph2 is completely within the horizontal bounds determined by the minimum X coordinate and maximum X coordinate of glyph1 directionalSignature glyph1 glyph2 sig Can be generated on demand by fire ask Low level presentation of the position relation between two glyphs The signature is a set of one or more numbers indicating the region in which glyph2 is relative to glyph1 1 is directly right of glyph1 2 is right and above 3 is directly above etc occludes glyph1 glyph2 glyph3 Can be generated on demand by fire ask Says that glyph1 is in a position between glyph2 and glyph3 such that it occludes each from the other In cases of partial occlusion this relationship holds if any of the following three conditions is true 1 More than 50 of the area of glyph1 lies in the visibility region between glyph2 and glyph3 i e more than
18. rigin Can be generated on demand by fire ask Indicates that in situation2 obj1 has been rotated around origin without translation from its orientation in situation1 blobIntersectsConvexHull glyph1 glyph2 Can be generated on demand by fire ask Says that the blob boundary of glyph1 intersects the convex hull of glyph2 lengthAlongMajorAxis obj distance Can be generated on demand by fire ask Gives the length of an object along its major axis in real world units 13 widthAcrossMajorAxis SpatialThing Distance Can be generated on demand by fire ask Gives the width of an object across its major axis in real world units majorAxisAngle glyph angle Can be generated on demand by fire ask Represents the major axis angle relative to the current 2D orientation of the glyph outsideNormal glyph surface qualitative vector Can be generated on demand by fire ask Says that the vector is the outside normal for the specified surface of a glyph The surface is an outside edge of a glyph computed via glyph decomposition overlappingParts glyph1 segment1 glyph2 segment2 Can be generated on demand by fire ask Says that glyph1 and glyph2 overlap and specifies the line segments where the overlap occurs qualitativeVectorBetween NuSketchPoint NuSketchPoint Qualitative Vector Can be generated on demand by fire ask qualitativeDirection is true iff the third argument is the qualitative direction from the first argument to the s
19. s based on the RCC 8 relations described above The first three are computed automatically and are used during comparison e g in worksheets and other applications The final two can be computed on demand Unlike RCC 8 these relations are not mutually exclusive For example if one glyph contains another they may also intersect If two glyphs are overlapping they will necessarily intersect containsObject glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Says that glyph1 contains glyph2 This is based on the RCC 8 relations rcc8 TPP and rcc8 NTPP Note that transitive containment is avoided That is if containsObject glyph1 glyph2 and containsObject glyph2 glyph3 hold then containsObject glyph1 glyph3 will not hold objectsintersect glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Says that the glyph1 and glyph2 s ink intersect This is based on the RCC 8 relations rcc8 EC rcc8 PO and rcc8 TPP Thus if the relation rcc8 TPP holds then both containsObject and objectsintersect will hold objectsOverlap glyph1 glyph2 Automatically computed between pairs of glyphs on same layer Says that the interiors of glyph1 and glyph2 overlap This is based on the RCC 8 relation rcc8 PO symmetricBisection glyph1 glyph2 Can be generated on demand by fire ask Says that the two glyphs overlap one another to the extent that each bisects the other objectContains Transitive glyph1
20. stOf southOf or southEastOf compassCentroidRelationFor obj1 obj2 rel Can be generated on demand by fire ask This is similar to compassPositionalRelationFor but only the centroids of the two glyphs are used to compute the compass positional relation ignoring the blob boundaries 10 5 2 5 GEOSPATIAL VIEW GENRE LOOKING FROM SIDE POSE positionalRelationFor obj1 obj2 rel Can be generated on demand by fire ask Says that the given positional relation holds between the two objects 5 2 6 GEOSPATIAL VIEW GENRE LOOKING FROM BOTTOM POSE positionalRelationFor obj1 obj2 rel Can be generated on demand by fire ask Says that the given positional relation holds between the two objects 5 2 7 ABSTRACT VIEW GENRE UNSPECIFIED VIEWPOINT POSE positionalRelationFor obj1 obj2 rel Can be generated on demand by fire ask Says that the given positional relation holds between the two objects 11 6 GLYPH GROUPS 6 1 CONTAINMENT isa ContainedGlyphGroupFn outside glyph TheList inside glyph1 inside glyph2 ContainedGlyphGroup Automatically computed between glyphs on a subsketch Reifies the glyphs contained inside another glyph thus allowing us to reason about the group as an entity containedGlyphGrouplnsider inside glyph glyph group Automatically computed between glyphs on a subsketch Says that inside glyph is one of the glyphs contained inside in the specified ContainedGlyphGroup containedGlyphGroupTangentiallns
21. the KB knowledge e The only visual relationships between glyphs that currently trigger this computation are touching and insideness i e RCC8 EC RCC8 PO RCC8 TPP RCC8 NTPP If you do not get possible relationships for a pair of glyphs check to see if one of these visual relationships holds and if not redraw or move one of them e If the set of relationship options does not include something that you think should be there check to see if that relationship is consistent with the types of entities involved using the KB Browser 15 9 RELATIONS USED IN SPATIAL ROUTINES The following four tables describe the attributes and relations used by Spatial Routines during cognitive modeling simulations e g see Perceptual Sketchpad and Geometric Analogy in the User Manual The first two tables describe the attributes and relations used to represent an image i e a sketch drawn in CogSketch or a psychological stimulus imported into CogSketch The latter two tables describe how routines represent a pattern of variance A pattern of variance describes the differences found between images It is used by Spatial Routines in some problem solving tasks such as geometric analogy and Raven s Progressive Matrices 9 1 OBJECT ATTRIBUTES Each object in an image i e each glyph in CogSketch is assigned a set of attributes from the following list Type General Shape Type Specific Shape Type Closedness Convexity Term 2D Shape Gen
22. to align isa Object A ScaledShape Bigger with isa Object 1 DeformedShape Longer because the two attributes share the generalized form TransformedShape Larger Type se Term Description A shape of type id id s are arbitrary Shape Type ShapeType ShapeTypeFn id numbers assigned to the shape types encountered in a given context A shape of type id that has been ShapeTransFn id transformed and or scaled from the trans scaling prototype for that type e g a circle that s bigger than the circles we ve seen before 19 Rotation Reflection Scaling Deformation Addition Other RotatedShape ReflectedShape Transformed Shape Larger Transformed Shape Smaller Transformed Shape Larger Transformed Shape Larger Transformed Shape Larger Transformed Shape Smaller Transformed Shape Smaller Transformed Shape Smaller RotatedShape 90 RotatedShape X ReflectedShape XAxis ReflectedShape YAxis ReflectedShape DiagAxis ReflectedShape Other ScaledShape Bigger ScaledShape Smaller DeformedShape Longer DeformedShape LongerPart DeformedShape AddedPart DeformedShape Shorter DeformedShape ShorterPart DeformedShape RemovedPart AddedShape RemovedShape ConstantShape A shape that s been rotated 90 degrees Some other rotation rounds to the nearest 45 degrees A shape that s been reflected over the x axis A shape that s been reflected over the y axis A shap
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