Knowledge Representation: Images and Propositions

Knowledge Representation:Images and Propositions Chapter 7

Outline • Mental Representation of Knowledge • Mental Manipulation of Images • Synthesizing Images and Propositions • Spatial Cognition and Cognitive Maps

1. Mental Representation of Knowledge 1. External Representations: Pictures Versus Words • Pictures • Analogous to the real-world object it represents • Shows concrete attributes (e.g. shape) that are similar to the features and properties of the real-world object the picture represents • Pictures aptly capture concrete and spatial information • Pictorial representations convey all features simultaneously

1. Mental Representation of Knowledge 1. External Representations: Pictures Versus Words • Words • Are symbolic representations • The relationship between the word and what it represents is simply arbitrary • Words capture abstract and categorical information in a manner that is symbolic of whatever they represent • Representations in words usually convey information sequentially, according to arbitrary rules of the symbol system for using words

1. Mental Representation of Knowledge 2. Mental Imagery • Imagery is the mental representation of things that are not currently being sensed by the sense organs • Mental imagery may represent things that have never been observed by our senses • Imagery may involve mental representations in any of the sensory modalities • Applications of mental imagery • Guided-imagery techniques for controlling pain, for strengthening immune responses, overcoming phobias

? Can you provide examples of mental imagery in all the sensory modalities?

1. Mental Representation of Knowledge 3. Dual-Code Theory: Analogical Images Versus Symbols • Dual-Code theory (Allan Paivio, 1969) • We use both images (in analogue codes) and words (in a symbolic code) for representing information • (investigating cognitive psychology, p. 218) • Visual images and words are separate codes • Visual imagery interferes with other visual tasks • Verbal tasks interfere with other verbal tasks • Visual imagery does not interfere with verbal tasks

? Which of the following tasks is (are) the hardest one(s)? • Imagine an elephant and at the same time try to draw a house. • Imagine the definition of “elephant” and at the same time write down a definition of short-term memory. • Draw an elephant and at the same time provide a definition of short-term memory.

1. Mental Representation of Knowledge 4. Propositional Theory • We do not store mental representations in the form of images; rather our mental representations more closely resemble the abstract form of a proposition • A proposition • The meaning underlying a particular relationship among concepts • Logicians have devised a shorthand means (called “predicate calculus”) of expressing the underlying meaning of a relationship • Propositions may be used to describe any kind of relationship, such as actions, attributes, positions, class memberships • Both images and verbal statements are mentally represented in terms of their deep meanings (as propositions) not as specific images or statements

? Look at Figure 7.4 (a) and imagine the rabbit shown in the figure. Without looking back at the figure, can you determine the alternative interpretation of Figure 7.4 (a)?

1. Mental Representation of Knowledge 4. Propositional Theory (cont.) • Ambiguous figure • It can be interpreted in more than one way • Not until you have in front of you an actual picture of the figure can you guess at an alternative interpretation of the figure • This indicates that mental representations of figures are not the same as percepts of these figures

2. Mental Manipulations of Images • Functional-equivalence hypothesis • Although we do not construct images that are exactly identical to percepts, we do construct images that are functionally equivalent to percepts • These functionally equivalent images are analogous to the physical percepts they represent

2. Mental Manipulations of Images 1. Mental Rotations • Functional-equivalence hypothesis does apply to image scaling • Participants were asked to observe pairs of two-dimensional (2-D) pictures showing three-dimensional (3-D) geometric forms • Participants then were asked to tell whether a given image was or was not a rotation of the original stimulus (p. 127) • The response times for answering the questions about the figures formed a linear function of the degree to which the figures were rotated; i.e. for each increase in the degree of rotation of the figures, there was a corresponding increase in the response times

2. Mental Manipulations of Images 2. Image Scaling • Functional-equivalence hypothesis does apply to image scaling • Seeing featural details of large objects is easier than seeing such details of small ones, and we respond more quickly to questions about large objects we observe than to questions about small ones we observe • If imaginal representation is functionally equivalent to perception, participants also should respond more quickly to questions about features of imaginally large objects than to questions about features of imaginally small ones • this prediction was confirmed

2. Mental Manipulations of Images 3. Image Scanning • Functional-equivalence hypothesis does apply to image scanning • Images, as spatial representations, can be scanned, much the same as physical percepts • Our strategies and responses for imaginal scanning are expected to be functionally equivalent to those we use for perceptual scanning

2. Mental Manipulations of Images 3. Image Scanning • Functional-equivalence hypothesis does apply to image scanning • In perception, to scan across longer distances takes longer than to scan across shorter ones • In image scanning • Participants were instructed that, on hearing the name of an object read to them, they should picture the map, mentally scan directly to the mentioned object, and press a key as soon as they arrived at the location of the named object (p. 233) • They found almost perfect linear relation between the distances separating objects in the mental map and the amount of time it took participants to press the button

3. Synthesizing Images and Propositions • Johnson-Laird’s Mental Models • Mental representations may take any of the three forms: • Propositions – fully abstracted representations of meaning • Mental models – knowledge structures that individuals construct to understand and explain their experiences • Images – much more specific representations, which retain many of the perceptual features of particular objects, viewed from a particular angle, with the particular details of a given instantiation

3. Synthesizing Images and Propositions • Experiments with blind people • They showed faster response times when scanning shorter distances than when scanning longer distances • At least in some respects, spatial imagery appears not to involve representations that are actual analogues to visual percepts; the use of haptic “imagery” suggests alternative modalities for mental imagery • Lateralization of function • Right hemisphere appears to be more proficient in representing and manipulating knowledge of visuospatial nature, whereas the left hemisphere appears to be more proficient in representing and manipulating verbal and other symbol-based knowledge

3. Synthesizing Images and Propositions • Patient L.H. (Farah, 1988) • Ability to see was intact • Could not recognize any of the pictures copied • Showed relatively normal abilities in performing tasks involving rotations, mental scanning, state locations • It seems like visual imagery can be dissociated from visual perception to some extent

4. Spatial Cognition and Cognitive Maps • Cognitive maps • Internal representations of our physical environment, particularly centering on spatial relationships • Rats, Bees, and Humans • Rats learning cognitive maps in maze tasks • Bees using different dances to represent different meanings • A round dance indicates a source less than 100 yards from the hive • A figure-eight dance indicates a source at a greater distance

4. Spatial Cognition and Cognitive Maps • Influences of semantic and propositional knowledge on imaginal representations • We have the tendency to enlarge the more prominent, well-known countries and diminish the sizes of less well-known countries • Drawing maps showing a Eurocentric view of the world • Sex differences in spatial and related skills • Women find it easier to remember where they saw things (spatial-location memory), whereas men find it easier to do mental rotations of spatial images • Men tend to perform better on common tests of spatial skills than do women

Knowledge Representation: Images and Propositions