348 Knowledge representation: categories
What, exactly is meant by the word ‘category’, whether in Aristotle or in Kant and Hegel,
I must confess that I have never been able to understand.
-- Bertrand Russell ( History of Western Philosophy)
Study of concepts & categories: several questions
how concepts are represented in terms of categories
how we classify instances/objects as belonging to a conceptual category
how we use concepts & categories in reasoning & problem solving
Category membership via definitions -- Aristotle through the 1950's
Aristotle --
"Classical approach" -- based on defining features
Categories are defined by a set of
necessary and sufficient features.
We develop rules that define categories based on that set of features.
This approach dominated thinking about categorization from Aristotle until the 1950's.
It's strongly appealing for several reasons:
It clearly explains how we decide whether an object belongs to a category
--objects with the necessary and sufficient features belong to the category,
--objects without those features are not members of the category.
Its explanation of category formation is intuitively appealing:
We form categories by encountering many objects, and discover those
"necessary & sufficient" features that divide the objects into separate classes.
An object has to have all of the defining features in order to be in the category
E.g., sorting cards into similar groups: black/spades -- red/hearts -- etc
Definitions are usually arbitrary, used for convenience
especially among experts
Definitions work well for highly structured & constrained categories
E.g., mathematical constructs, geometry
Problems:
People usually unable to identify the defs they use for most categories (McNamara & Sternberg, 1983)
Dfinitions often vary across people for the same category, and for the same person over time (Rosch, 1975)
So how can we communicate effective if our notions of categories are based on inconsistent definitions!
Empirical research to test the definition approach have not supported it (Fodor, et al, 1980: "Against Definitions")
E.g., since "male" is part of the definition of "bachelor," it's a simpler construct than is bachelor.
Thus, we'd expect response times in categorization tasks to "male" to be faster than to "bachelor."
But that turned out to be untrue -- response times are about the same.
Empirical research on categorization often reveals "typicality" effects, which are not rule-based (Rosch, 1973)
E.g,,"robin" is more typical of the category "birds" than is "emu," though they are both clearly birds.
Such effects are very strong & persistent across many research projects.
If our categorizations were based on a set of defining rules, typicality effects should not occur.
Definitions don't work so well for "natural" and "everyday" categories
They are "fuzzy" in the sense that it's hard to establish clear, defining rules for all instances of a category.
That is, some items might be either in category A or else in category B
Wittgenstein: Those dreadful, uncooperative games
Solution: Family resemblances
Categories via "family resemblance" -- two approaches
Prototypes -- Eleanor Rosch & Carolyn Mervis (1975), and many others
We store an “average” image of a class of objects
The “average” is an abstraction
It may not actually exist in the natural world
C.f., Plato's "ideal forms"
Category boundaries are expected to be "fuzzy," not sharply defined
Categories share some characteristic properties, attributes, or features
A particular object doesn't have to have all the common properties to be in the category
Recognition occurs when we match an object to a prototype
Similar to template theory, but more parsimonious:
doesn’t require a vast # of individual items in memory
more flexible, since the prototype is readily updated with new experiences
Prototypical objects = objects highly similar to the prototype
Prototypical objects = quick & easy recognition
Objects not very similar to prototype = slow & uncertain recognition
Prototypical objects = named first in a listing task
Prototypical objects = affected more by priming than are non-prototypical objects
Prototypes vary with personal experience as well as across different cultures
E.g., your idea of a prototypical bird might differ from mine
Strengths:
accounts for many "everyday" and "natural" categories
accounts for "typicality" effects
accounts for differing notions of category membership, across people &/or across time
much empirical research supports this approach
Problems: its strength is also its weakness:
Going for “average” means individual features are often discarded
Thus misrecognition can occur when a specific object is not very similar to the prototype
Communication difficulties arise when category inclusion differs for different people
Exemplars -- Robert Nosofsky (1991) & others
Whereas prototypes are abstract "ideals," exemplars are real members of a category.
These exemplars are learned from personal experience
They are stored in memory & are used for comparisons with new objects
A new object is compared to one or more exemplars of a category.
Strengths:
Same as those for prototype approach!
Problems:
Similar to those for prototypes, except that discarding individual features is not a problem
Misrecognitions arise when the exemplars are inadequate to determine the category
especially for objects from the "fuzzy" boundary of the category
Unclear how categories are originally formed
Has the risk of requiring large # of exemplars to account for all instances of a category
Combining/comparing prototypes & exemplars
“We know generally what cats are (the prototype),
but we know specifically our own cat is the best (an exemplar).”
-- Minda & Smith (2001)
Some theorists argue that we use both approaches:
Exemplars seem to work better for tasks involving smaller-sized categories
Prototypes seem to work better for tasks involving larger-sized categories
Exemplar seem to provide a better account for recognizing atypical instances of a category
As we might divine from the foregoing, similarity theories of categorization have run into a sort of "dead end."
They are pretty good at accounting for much of categorization effects, as usually discussed,
but the two major approaches cannot be readily distinguished in terms of their strengths & weaknesses.
Recent approaches -- Douglas Medin (1980's & 1990's) & many others
The foregoing approaches have tended to focus on classification, and features
They also assume that categories are (1) natural and hence can be studied by ordinary empirical science
and (2) that all categories are based on a particular model, e.g., defining features, exemplars, or else prototypes
Current thinking about categorization has begun to challenge those foci & assumptions
Much recent work started with an influential paper by Greg Murphy and Doug Medin (1985):
Coherence is an integral aspect of categories, but ignored by the foregoing approaches
Other theorists note that the foregoing approaches emphasize objects, ignoring other ways of thinking about the world
E.g., relations based on roles or relations (emphasizing verbs rather than objects)