9. MENTAL REPRESENTATION OF KNOWLEDGE
Knowledge Structure
Declarative Knowledge can be stated (Knowing That)
Procedural Knowledge can be implemented (Knowing How)
Pictures vs. Words
Knowledge can be represented in different ways in your mind: It can be stored as a mental
picture, or in words, or abstract propositions.
Some ideas are better and more easily represented in pictures, whereas others are better
represented in words. (like justice, freedom and …)
The picture is relatively Analogous (i.e., similar) to the real world object it represents and there
are no arbitrary rules for looking at the picture.
10. MENTAL REPRESENTATION OF KNOWLEDGE
Symbolic Representation
The word “cat” is a symbolic representation, meaning that the relationship between the word
and what it represents is simply arbitrary. There is nothing inherently catlike about the word.
Because symbols are arbitrary, their use requires the application of rules.
Summarize
Pictures Words
Objective, Concretive Subjective, Abstractive
Spatial Categorical
Parallel Serial
11. MENTAL IMAGERY
Definition
Imagery is the mental representation of things that are not currently seen or sensed by the sense
organs or represent things that you have never experienced. for example: Sphinx, Unicorn,
Centaur and …
Imagery may (or must?) involve mental representations in any of the sensory modalities, such as
hearing, smell, or taste.
12. DUAL-CODE THEORY
According to dual-code theory, we use both pictorial and verbal codes for
representing information in our mind. (Paivio)
Pictorial: Mental images are analog codes. Analog codes resemble the objects they are
representing. Then the mental images we form in our minds are analogous to the physical stimuli
we observe.
Verbal: Our mental representations for words chiefly are represented in a symbolic code. A
symbolic code is a form of knowledge representation that has been chosen arbitrarily to stand
for something that does not perceptually resemble what is being represented.
Verbal information seems to be processed differently than pictorial
information.
13. PROPOSITIONAL THEORY
Propositional theory suggests that we do not store mental representations in the
form of images or mere words. We may experience our mental representations as
images, but these images are epiphenomena (or secondary) and derivative
phenomena that occur as a result of other more basic cognitive processes.
Logical approach
[Relationship between elements]([Subject element], [Object element])
Propositions may be used to describe any kind of relationship.
Any number of propositions may be combined to represent more complex relationships, images,
or series of words.
15. PROPOSITIONAL THEORY
Limitations of Mental Images
In defense of propositional theory:
Much earlier work suggested that semantic
(verbal) information (e.g., labels for figures) tends
to distort recall of visual images in the direction
of the meaning of the images.
16. PROPOSITIONAL THEORY
Limitations of Propositional Theory
Imaginal Gestalt experience: In the combined image, the whole of the two combined images
differed from the sum of its two distinct parts.
17. PROPOSITIONAL THEORY
Mental reinterpretation of ambiguous figures
The first is a mental realignment of the reference
frame. This realignment would involve a shift in the
positional orientations of the figures on the mental
“page” or “screen” on which the image is displayed.
The duck’s back to the rabbit’s front
The second manipulation is a mental reconstrual
(reinterpretation) of parts of the figure.
The duck’s bill as the rabbit’s ears
18. MENTAL MANIPULATIONS OF IMAGES
Functional-Equivalence Hypothesis
According to the functional-equivalence hypothesis, we represent and use visual imagery in a way
that is functionally equivalent (strongly analogous) to that for physical percepts.
Finke’s principles of visual imagery:
1) Our mental transformations of images and our mental movements across images correspond to
those of physical objects and percepts.
2) The spatial relations among elements of a visual image are analogous to those relations in actual
physical space.
3) Mental images can be used to generate information that was not explicitly stored during
encoding.
4) The construction of mental images is analogous to the construction of visually perceptible figures.
5) Visual imagery is functionally equivalent to visual perception in terms of the processes of the
visual system used for each.
19. MENTAL ROTATIONS
Mental rotation involves rotationally transforming an object’s visual mental image.
Response times to questions about mental rotations of figures show a linear relationship
to the angle of rotation, and this relationship is preserved, whether the rotations are in
the picture plane or are in depth.
20. IMAGE SCALING
The main concept: Our resolution is limited
if we assume that perception and mental
representations are functionally equivalent, then
participants should respond more quickly to
questions about features of large imagined objects
than to questions about features of small ones.
21. IMAGE SCANNING
The main concept: Images scanned like physical percepts
For example, in perception, to scan across longer distances
takes longer than to scan across shorter ones. (Linear relation)
If we did not use a spatial representation but rather a code
based propositional theory, then the distance between the
points should not have influenced reaction time, but it did.
22. SYNTHESIZING IMAGES AND PROPOSITIONS
Johnson-Laird’s Mental Models
Mental representations may take any of three forms:
Propositions
Images
Mental models
Mental Model: Mental models are knowledge structures that individuals construct to understand
and explain their experiences. The models are constrained by the individuals’ implicit theories
about their experiences. (Belief, perspective)
Faulty mental models are responsible for many errors in thinking and experience is a useful tool
for the repair of faulty mental models.
Mental models provide a way of explaining empirical findings, such as haptic and auditory
forms of imagery, which seem quite different from visual images.
23. LATERALIZATION OF FUNCTION
The right hemisphere appears to represent and manipulate visuospatial knowledge in a manner
similar to perception. In contrast, the left hemisphere appears to be more proficient in
representing and manipulating verbal and other symbol-based knowledge.
Perhaps cerebral asymmetry has evolutionary origins. The right hemisphere of the human brain
represents knowledge in a manner that is analogous to our physical environment.
Visual versus Spatial
Visual imagery refers to the use of images that represent visual characteristics such as colors
and shapes. Spatial imagery refers to images that represent spatial features such as depth
dimensions, distances, and orientations.
24. CASE OF L.H
Damaged regions of the brain:
The right temporal lobe and right inferior frontal lobe, as shown in the figure at the right; and the
temporo-occipital region, as shown in the figure at the left.
25. CASE OF L.H
L. H. was able to draw accurately various objects.
Panel (a) shows what he was shown, and panel (b)
shows what he drew. However, he could not recognize
the objects he copied. Despite L. H.’s severe deficits on
visual-imagery tasks [panel (c), regarding colors,
sizes, shapes, etc.], L. H. showed normal ability on
spatial-imagery tasks [panel (d) regarding rotations,
scanning, scaling, etc.].
He was able satisfactorily to copy various pictures.
Nonetheless, he could not recognize any of the
pictures he copied. In other words, he could not link
verbal labels to the objects pictured.
26. SPATIAL COGNITION AND COGNITIVE MAPS
Cognitive maps are internal
representations of our physical
environment, particularly centering on
spatial relationships and simulate
particular spatial features of our
external environment.
Edward Tolman found that rats
seemed to have formed a mental
map of a maze during behavioral
experiments.
With just one reinforcement, the
learning of these rats improved
dramatically.
27. SPATIAL COGNITION AND COGNITIVE MAPS
Humans seem to use three types of knowledge when forming and using cognitive maps:
1) Landmark knowledge is information about particular features at a location and which may be
based on both imaginal and propositional representations.
2) Route-road knowledge involves specific pathways for moving from one location to another .It
may be based on both procedural knowledge and declarative knowledge.
3) Survey knowledge involves estimated distances between landmarks, much as they might appear
on survey maps. It may be represented imaginally or propositionally (e.g., in numerically
specified distances).
28. RULES OF THUMB
When we use landmark, route-road, and survey knowledge, we sometimes use rules of thumb that
influence our estimations of distance. These rules of thumb are cognitive strategies termed heuristics.
For example, in regard to landmark knowledge, the density of the landmarks sometimes appears to
affect our mental image of an area.
In estimations of distances between particular physical locations (e.g., cities), route-road knowledge
appears often to be weighted more heavily than survey knowledge.
The use of heuristics in manipulating cognitive maps suggests that propositional knowledge affects
imaginal knowledge.
Conceptual information seems to distort mental images. In these situations, propositional strategies
may better explain people’s responses than strategies that are based on a mental image.
29. RULES OF THUMB
The distortions seem to reflect a tendency to regularize features of mental maps. Thus, angles, lines, and
shapes are represented as more like pure abstract geometric forms than they really are.
1) Right-angle bias: People tend to think of intersections as forming 90-degree angles more often than
the intersections really do.
2) Symmetry heuristic: People tend to think of shapes as being more symmetrical than they really are.
3) Rotation heuristic: When representing figures and boundaries that are slightly slanted, people tend
to distort the images as being either more vertical or more horizontal than they really are.
4) Alignment heuristic: People tend to represent landmarks and boundaries that are slightly out of
alignment by distorting their mental images to be better aligned than they really are.
5) Relative-position heuristic: The relative positions of particular landmarks and boundaries is
distorted in mental images in ways that more accurately reflect people’s conceptual knowledge
about the contexts in which the landmarks and boundaries are located, rather than reflecting the
actual spatial configurations.
31. RULES OF THUMB
Semantic or propositional knowledge (or beliefs) can also influence our imaginal representations of
world maps. Students from 71 sites in 49 countries were asked to draw a sketch map of the world.
Most students (even Asians) drew maps showing a Eurocentric view of the world.
32. TEXT MAPS
We may be able to create cognitive maps from a verbal description. These cognitive maps may be
as accurate as those created from looking at a graphic map.
SOUND MAP
34. COMBINING REPRESENTATIONS
Knowledge Representation:
Semantic-Network Models (Declarative Knowledge)
Serial Information-Processing Models (Procedural Knowledge)
In ACT model, John Anderson synthesized some of the features of
serial information-processing models and some of the features of
semantic-network models.
In ACT model, procedural knowledge is represented in the form of
production systems. Declarative knowledge is represented in the
form of propositional networks.
John R. Anderson
Carnegie Mellon University
35. SEMANTIC-NETWORK MODELS
Semantic-network models suggest that
knowledge is represented in our minds in
the form of concepts that are connected
with each other in a web-like form and
knowledge is represented in terms of a
hierarchical semantic network.
The elements are called nodes; they are
typically concepts. The connections between
the nodes are labeled relationships.
36. SEMANTIC-NETWORK MODELS
Cognitive Economy
Within a hierarchy, we can efficiently store information that applies to all members of a
category at the highest possible level in the hierarchy. We do not have to repeat the
information at all of the lower levels in the hierarchy. Therefore, a hierarchical model provides
a high degree of cognitive economy.
Inheritance
Whatever was known about items at higher levels in a hierarchy was applied to all items at
lower levels in the hierarchy. This concept of inheritance implies that lower-level items inherit the
properties of higher-level items.
37. ACT-R
The most recent version of ACT, ACT-R (where the R stands for rational), is a model
of information processing that integrates a network representation for declarative
knowledge and a production-system representation for procedural knowledge.
In ACT-R, networks include images of objects and corresponding spatial
configurations and relationships. They also include temporal information, such as
relationships involving the sequencing of actions, events, or even the order in which
items appear. The temporal information (or temporal strings) contain information
about the relative time sequence.
38. HOW ACT-R WORKS
ACT-R’s main components are:
Modules:
• Perceptual-Motor Modules
• Memory Modules:
• Declarative Memory
• Procedural Memory
Buffers
Pattern Matcher
40. MARR’S MODEL
Marr's three levels of analysis:
Computational: At this level we describe and specify the problems we are faced with in a
generic manner, but do not say how these problems are to be solved.
Algorithmic: This level forms a bridge between the computational and implementational levels,
describing how the identified computational problems can be solved.
Implementational: The physical substrate or mechanism, and its organisation, in which
computation is performed. This could be biological in the case of neurons and synapses, or in
silicon using transistors, etc.
Marr’s computational analysis of visual system
The visual system’s job is to provide a 3D representation of the visual environment that can serve
as input to recognition and classification processes – primarily information about shape of
objects and their spatial distribution.
This 3D representation is on an object-centered rather than viewer-centered frame of reference.
42. MARR’S MODEL
Primal Sketch
Identifies intensity changes in the 2D
image.
Basic information about the geometric
organization of those intensity changes.
Primitives include:
Zero-crossings
Virtual lines
Groups
43. MARR’S MODEL
Zero crossings (Edge Detection)
If we plot changes in intensity on a graph, then radical discontinuities will be signalled by the
curve crossing zero. Marr proposed a Laplacian/Gaussian filter (Spatial filter) to detect zero
crossings.
44. MARR’S MODEL
2½-D sketches
Displays orientation of visible surfaces
in viewer-centered coordinates
Represents distance of each point in
visual field from viewer
Also orientation of each point and
contours of discontinuities
Very basic information about depth
45. MARR’S MODEL
3D sketch
Characterizes shapes and their spatial
organization
Object-Centered (Previous knowledge
is important)
