Prototype theory

Prototype Theory is a model of graded categorization in Cognitive Science, where some members of a category are more central than others. For example, when asked to give an example of the concept furniture, chair is more frequently cited than, say, stool. Prototype theory also plays a central role in Linguistics, as part of the mapping from phonological structure to semantics.

As formulated in the 1970s by Eleanor Rosch and others, prototype theory was a radical departure from traditional necessary and sufficient conditions as in Aristotelian logic, which led to set-theoretic approaches of extensional or intensional semantics. Thus instead of a definition based model - e.g. a bird may be defined as elements with the features [+feathers], [+beak] and [+ability to fly], prototype theory would consider a category like bird as consisting of different elements which have unequal status - e.g. a robin is more prototypical of a bird than, say a penguin. This leads to a graded notion of categories, which is a central notion in many models of cognitive science and cognitive semantics, e.g. in the work of George Lakoff (Women, fire and dangerous things, 1987) or Ronald Langacker (Cognitive Grammar, vol. 1/2 1987/1991).

The term prototype has been defined in Eleanor Rosch's study "Natural Categories" (1973) and was first defined as a stimulus, which takes a salient position in the formation of a category as it is the first stimulus to be associated with that category. Later, she redefined it as the most central member of a category.

Cognitive Representation of Semantic Categories

In her 1975 paper, Cognitive Representation of Semantic Categories (J Experimental Psychology v. 104:192-233), Eleanor Rosch asked 200 American college students to rank, on a scale of 1 to 7, whether they regarded the following items as a good example of the category furniture. The resulting ranks are as follows:

1 chair

1 sofa

3 couch

3 table

5 easy chair

6 dresser

6 rocking chair

8 coffee table

9 rocker

10 love seat

11 chest of drawers

12 desk

13 bed

...

22 bookcase

27 cabinet

29 bench

31 lamp

32 stool

35 piano

41 mirror

42 tv

44 shelf

45 rug

46 pillow

47 wastebasket

49 sewing machine

50 stove

54 refrigerator

60 telephone

While one may differ from this list in terms of cultural specifics, the point is that such a graded categorization is likely to be present in all cultures. Further evidence that some members of a category are more privileged than others came from experiments involving:

1. Response Times: in which queries involving a prototypical members (e.g. is a robin a bird) elicited faster response times than for non-prototypical members.

2. Priming: When primed with the higher-level (superordinate) category, subjects were faster in identifying if two words are the same. Thus, after flashing furniture, the equivalence of chair-chair is detected more rapidly than stove-stove.

3. Exemplars: When asked to name a few exemplars, the more prototypical items came up more frequently.

Subsequent to Rosch's work, prototype effects have been investigated widely in areas such as colour cognition (Brent Berlin and Paul Kay, 1969), and also for more abstract notions. Subjects may be asked, e.g. "to what degree is this narrative an instance of telling a lie?" [Coleman/Kay:1981]. Similarly work has been done on actions (verbs like look, kill, speak, walk [Pulman:83]), adjectives like "tall" [Dirven/Taylor:88], etc.

Another aspect in which Prototype Theory departs from traditional Aristotelian categorization is that there do not appear to be natural kind categories (bird, dog) vs. artefacts (toys, vehicles).

Basic Level Categories

The other notion related to prototypes is that of a Basic Level in cognitive categorization. Thus, when asked What are you sitting on?, most subjects prefer to say chair rather than a subordinate such as kitchen chair or a superordinate such as furniture. Basic categories are relatively homogeneous in terms of sensori-motor affordances - a chair is associated with bending of one's knees, a fruit with picking it up and putting it in your mouth, etc. At the subordinate level (e.g. [dentist's chairs], [kitchen chairs] etc.) hardly any significant features can be added to that of the basic level; whereas at the superordinate level, these conceptual similarities are hard to pinpoint. A picture of a chair is easy to draw (or visualize), but drawing furniture would be difficult.

Rosch (1978) defines the basic level as that level that has the highest degree of cue validity. Thus, a category like [animal] may have a prototypical member, but no cognitive visual representation. On the other hand, basic categories in [animal], i.e. [dog], [bird], [fish], are full of informational content and can easily be categorised in terms of Gestalt and semantic features.

Clearly semantic models based on attribute-value pairs fail to identify privileged levels in the hierarchy. Functionally, it is thought that basic level categories are a decomposition of the world into maximally informative categories. Thus, they

• maximize the number of attributes shared by members of the category, and
• minimize the number of attributes shared with other categories

However, the notion of Basic Level is problematic, e.g. whereas dog as a basic category is a species, bird or fish are at a higher level, etc. Similarly, the notion of frequency is very closely tied to the basic level, but is hard to pinpoint.

More problems arise when the notion of a prototype is applied to lexical categories other than the noun. Verbs, for example, seem to defy a clear prototype: [to run] is hard to split up in more or less central members.

Distance between Concepts

The notion of prototypes is related to Wittgenstein's (later) discomfort with the traditional notion of category. This influential theory has resulted in a view of semantic components more as possible rather than necessary contributors to the meaning of texts. His discursion on the category game is particularly incisive (Philosophical Investigations 66, 1953):

Consider for example the proceedings that we call `games'. I mean board games, card games, ball games, Olympic games, and so on. What is common to them all? Don't say, "There must be something common, or they would not be called `games' " - but look and see whether there is anything common to all. For if you look at them you will not see something common to all, but similarities, relationships, and a whole series of them at that. To repeat: don't think, but look! Look for example at board games, with their multifarious relationships. Now pass to card games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball games, much that is common is retained, but much is lost. Are they all `amusing'? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear. And the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail.

Clearly, the notion of family resemblance is calling for a notion of conceptual distance, which is closely related to the idea of graded sets, but there are problems as well.

Recently, Peter Gardenfors (Conceptual Spaces, MIT Press 2000) has elaborated a possible implementation to prototype theory in terms of multi-dimensional feature spaces, where a category is defined in terms of a conceptual distance. More central members of a category are "between" the peripheral members. He postulates that most natural categories exhibit a convexity in conceptual space, in that if x and y are elements of a category, and if z is between x and y, then z is also likely to belong to the category.

However, In the notion of game above, is there a single prototype or several? Recent linguistic data from colour studies seem to indicate that categories may have more than one focal element - e.g. the Tsonga colour term rihlaza refers to a green-blue continuum, but appears to have two prototypes, a focal blue, and a focal green. Thus, it is possible to have single categories with multiple, disconnected, prototypes, in which case they may constitute the intersection of several convex sets rather than a single one.

Combining Categories

All around us, we find instances where objects like tall man or small elephant combine one or more categories. This was a problem for extensional semantics, where the semantics of a word such as red is to be defined as the set of objects having this property. Clearly, this does not apply so well to modifiers such as small; a small mouse is very different from a small elephant.

These combinations pose a lesser problem in terms of prototype theory. In situations involving adjectives (e.g. tall), one encounters the question of whether or not the prototype of [tall] is a 6 feet tall man, or a 400 feet skyscraper [Dirven and Taylor 1988]. The solution emerges by contextualizing the notion of prototype in terms of the object being modified. This extends even more radically in compounds such as red wine or red hair which are hardly red in the prototypical sense, but the red indicates merely a shift from the prototypical colour of wine or hair respectively. This corresponds to de Saussure's notion of concepts as purely differential: "non pas positivement par leur contenu, mais negativement par leurs rapports avec les autres termes du systeme" [p.162; not positively, in terms of their content, but negatively by contrast with other terms in the same system (tr. Harris 83)].

Other problems remain - e.g. in determining which of the constituent categories will contribute which feature? In the example of a "pet bird" [Hampton 97], pet provides the habitat of the compound (cage rather than the wild), whereas bird provides the skin type (feathers rather than fur).

Literature

• John R. Taylor, 2003, Linguistic Categorization, Oxford University Press.
• Berlin, B., P. Kay (1969): Basic Color Terms: Their Universality and Evolution, Berkeley.
• Dirven, R./Taylor, J.R. (1988). "The conceptualisation of vertical Space in English: The Case of Tall", Brygida Rudzka-Ostyn (ed). Topics in Cognitive Linguistics. Amsterdam.
• Lakoff, G. (1987): Women, fire and dangerous things: What categories reveal about the mind, London.
• Rosch, E. Heider (1973). "Natural categories", Cognitive Psychology 4, 328 - 350.
• Rosch, E. (1975): “Cognitive reference points”, Cognitive Psychology 7, 532-547.
• Wittgenstein, L. (1997): „Philosophische Untersuchungen“, in: Tractatus Logico-Philosophicus, 1, Frankfurt, 225-580.