1. Category: `a group of objects that are considered equivalent - generally designated by a name (that is, a word).'
2. Concept: `a mental representation of such a group which may or may not have an associated word'
3. What kinds? Most researchwork has been about natural kinds and artifacts. Roughly things, relations, episodes.
4. What are categories useful for?
1. perceptual efficiency (since there are fewer category types than realworld objects)
2. quick inference (since category membership implies many relevant properties about things)
3. support combinatory operations (by allowing construction of phrases, sentences, texts, etc)
1. The meaning of a concept can be captured by a conjunctive list of attributes. Eg, Chair = (4-legs AND chairback AND seat AND...)
2. The attributes (including atomic primitives) are the building blocks of concepts and categories.
3. The attributes are singly necessary and jointly sufficient to specify each concept. So X is not a mother unless Female AND Parent, and any female parent is a mother.
Therefore this implies that:
4. What is or is not a category member should be clearcut, not graded or fuzzy.
5. All members should be equally representative of the category (none should be more or less typical)
6. Similarity of category members should be symmetrical. If A is like B, then B should be equally similar to A, since they are defined by the same list of definitional properties.
7. When categories are organized into a hierarchy, higher levels have fewer attributes than lower levels. Thus, `furniture' should be defined in more general terms than, say, `chair' or `table.'
However, these predictions often fail. For example, see Rosch studies showing members may be more or less typical, and frequent cases of similarity anomalies.
BASIC Level (dog, chair, tree). Basic categories are faster to name, acquired first by children, and most commonly used.
SUPERORDINATE Level (animal, furniture, plant)
SUBORDINATE (Collie, desk chair, pinetree)
Similarity based on Coordinate Spaces.
How can categories be compared? Are cats locations in a coordinate space (eg, color, pitch,sweetness, etc)? If so, then distance measures would be straightforward. This seems appealing but is not plausible for most categories. Even when plausible, the `metric assumptions' that apply intuitively in Euclidean space often do not work as expected: If d(i,j) is `the distance from i to j', then:
1. minimality: d(i,j) >= d(i,i) = 0
2. symmetry: d(i,j) = d(j,i)
3. triangle inequality: d(i,j) + d(j,k) >= d(i,k)
Non-symmetry is prevalent in linguistic expressions. `i is like j' i= subject, target, variant, new, less salient j = referent, prototype, standard, more salient. Examples:
`N. Korea is like China' but not `China is like N. Korea' `
The Indians fought like wildcats' but not ?`The wildcats fought like Indians'
`The boy looks/acts like his Dad' but not ?`Dad looks/acts like his son'
Intransitivity is also common.
Jamaica is similar to Cuba. Cuba is similar to Russia. But Jamaica is not similar to Russia.
(In this case, the criteria for comparision have obviously shifted between the first and second sentence - from geography to politics.)
Similarity based on Feature Sets
So Amos Tversky (1977, Psych Rev) made a strong case that:
(1) similarity is best interpreted in terms of collections of features (eg, components, properties, attributes, etc) possessed by the categories being compared.
(2) better known categories tend to have more features than less familiar categories. Let I = set of features of i, and J = feature set of j.
(3) the similarity of i to j: s(i,j) = some function of (I INTRSCT J, I-J, J-I) So similarity is measured by matching up and comparing both feature sets.
The Contrast Model (includes additional assumptions)
s(i,j) = af(I INTRSCT J) - bf(I-J) - cf(J-I)
where f weights apriori importance of specific feature sets, and weights a,b,c weight the importance of common vs. distinct features in a particular comparison task (depending on how the comparison question is asked).
If b > c (eg, if the subject is weighted more heavily than the referent), then the similarity is reduced more by the distinctive features of the subject (I-J) than by the distinctive features of the referent (J-I). Thus `An ellipse is similar to a circle' is more true than `A circle is similar to an ellipse', since in this kind of comparison sentence, b>c. But for the question `How similar are a circle and ellipse to each other', then necessarily b=c (that is, symmetry is presumed).
If feature lists for a set of categories are obtained from a group of Ss (and then cleaned up somehow), and then Ss (either same or different set) are asked similarity questions about the categories, the Context Model tends to be supported quite well (assuming reasonable settings for f and coefficients a,b,c).
R. Port, 1999 Intro to Cognitive Science Q500