Lecture 8.3: concepts
— what everyone knows
— the structure of concepts
— learning concepts
— the computational principles behind concepts
the knowledge basis of common sense
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Kinds and categories. To serve as a teacup, an
object must have certain features: hold liquid, have a
handle, etc. (defaults). Not all of these are obligatory:
a traditional Chinese teacup has no handles (defaults are
defeasible). A teacup is a kind of cup; a
cup is a kind of liquid container (hierarchy).
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Space and time. One's home is usually in a
particular place. To get from one place to another, objects
must undergo movement. There cannot be more than one solid
object in the same place at the same
time. If an inanimate object is in a particular
place at a given time, it will be there at a
future time, unless moved.
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Cause and effect. Despite the constant attempts on the
part of the four-year-olds all over the world to convince their
caregivers otherwise, things don't become broken without
outside intervention.
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Goals and plans. Certain kinds of objects such
as people and animals have desires; those
that do may also have goals and some can even plan
their behavior accordingly.
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Scripts and strategies. Many kinds of events
typically unfold according to rather rigid scripts, the knowledge of
which is critical for planning the behavior of self and
understanding the behavior of others.
a tangled hierarchy of concepts
A tiny portion of the enormous
network of concepts a
variant of which resides in every person's memory.
Some of the bottom-level nodes label features, others parts.
The links are dynamic (they depend on past experience and
on the current goal context) and are graded rather than
all-or-none.
slide 3
two of the many possible uses of cow
Context dependency of concepts:
cow may be categorized both under
food and under projectile (to catapult a cow, use a large
trebuchet).
slide 4
concepts: "vertical" structure
In concept structure, it is possible to distinguish between a
vertical dimension, which pertains to the "domination" or
inclusion relationships between categories, and a horizontal
dimension, having to do with the relationships of concepts that belong to
the same category.
Basic level of categorization.
slide 6
concepts: "horizontal" structure
In concept structure, it is possible to distinguish between a
vertical dimension, which pertains to the "domination" or
inclusion relationships between categories, and a horizontal
dimension, having to do with the relationships of concepts that belong to
the same category.
Prototypes and the radial structure of categories:
cow vs. llama as a farm animal.
natural kinds and others
A
natural
kind:
iron.
Something else: game.
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 that is common to all,
but similarities, relationships, and a whole series of them
at that.
Ludwig Wittgenstein, Philosophical Investigations, 66.
slide 8
concepts: the view from here (Barsalou et al.)
An average between-subjects correlation in concept-related tasks of only
0.50; this in addition to significant within-subject variability over of
time (0.80 correlation).
Different groups of subjects (such as faculty and undergraduate students,
or people of different ethnicities) yielded distinct patterns of
categorization.
Interestingly, members of each group were quite good (and consistent) in
assuming the point of view of other groups.
slide 9
concepts: the view from here
— In a study at Emory, faculty and undergraduate students generated
graded structures for various categories.
— Across, categories, the average correlation between faculty- and
undergrad-generated structure was 0.23.
— However, structure generated by undergrads from the faculty's point
of view was identical to that generated by the faculty. Structure
generated by faculty from ugrad point of view was very similar to that
generated by the ugrads themselves.
— Graduate students were perfect in taking the points of view of both
faculty and undergrads.
Barsalou and Sewell (1984)
slide 10
concepts and the causal stucture of the world
A
graphical model is a probabilistically annotated
graph that represents causal relationships among some variables pertaining
to the state of affairs in the world. One type of such model is the
Bayes
network.
"Hidden" variables cannot be observed directly, only inferred from
measurements (M) carried out on the observables.
Bottom left: in this two-node graphical model, the variables
A and B are independent (no arc between them).
Bottom center: B depends on A.
Bottom right: A and B are conditionally independent,
given C.
slide 11
concepts: an interim computational summary
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Exemplars. Conceptual memory is formed by processing
perceptual exemplars through abstraction and integration. Exemplars
are initially retained through the mechanisms of simple memory
(imprinting).
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Probabilities. The computational process whereby
generalities, if any, are abstracted and multiple exemplars
integrated is statistical inference (entrenchment).
When applied to memory structures, it can be viewed as purposive
modification of the representational energy landscape.
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Context. Because memory is always for something,
the details of the hierarchically structured generalizations depend
on the task. Computationally, this dependence can be expressed in the
language of conditional probability.
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Interconnectedness. The brain supports such fluidity by linking
the representations of concepts together into a highly ramified
network. The conditional probabilities control the strength of
network links, and are subject to change through experience (e.g.,
through the acquisition of new exemplars).
