Lecture 8.3      Last modified on Mon Oct 22 09:16:26 2007

Lecture 8.3: concepts

— the structure of concepts

— learning concepts

— the computational principles behind concepts

the knowledge basis of common sense

• 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).
• 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.
• 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.
• 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.
• 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

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:

slide 4

a cow as a projectile

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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.

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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.

slide 7

natural kinds and others

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.

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concepts: the view from here (Barsalou et al.)

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.

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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.

slide 10

concepts and the causal stucture of the world

"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.

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concepts: an interim computational summary

• Exemplars. Conceptual memory is formed by processing perceptual exemplars through abstraction and integration. Exemplars are initially retained through the mechanisms of simple memory (imprinting).
• 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.
• 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.
• 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).