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Cognitive science

The logic of human learning

Nature volume 407, pages 572–573 (2000)Cite this article

We view the world not as a continuous flux, but in terms of discrete, labelled categories, such as tables, trees and teapots. These categories are by no means arbitrary — a 'pseudo'-category consisting of an arbitrary assortment of objects starting with the letter 't' would not only be extremely difficult to learn, it would be hard to remember and to interpret in new situations. But what makes some categories 'better' than others? Why are we disposed to divide the world into teapots and not 't-words'? On page 630 of this issue, Jacob Feldman1 takes an important step towards answering this question. He suggests that there is a formal measure of complexity that determines how natural a category is and how difficult it is to learn.

Feldman pursues the intuitively attractive idea that simple boolean concepts are the easiest to learn. But how can complexity be measured? First, the complexity of a logical formula is defined as the number of non- logical terms (the primitive features a, b and c) that occur in that formula — this measure is boolean complexity. So, for example, the formula (a AND b) OR (a AND (NOT b)) would have a boolean complexity of 4. Second, we can define the complexity of a boolean concept as the minimal complexity of any logical formula that expresses that concept. The boolean concept associated with (a AND b) OR (a AND (NOT b)) can most simply be expressed by a very simple formula: a. Hence it has a boolean complexity of 1. Feldman presents impressive experimental data showing that the greater the boolean complexity of a concept, the harder it is to learn. So it seems that boolean complexity provides a measure of the 'naturalness' of a concept.

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Figure 1: Learning complex rules.
Figure 2: Simplicity in perception.

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  1. Department of Psychology, University of Warwick, Coventry, CV4 7AL, UK

    Nick Chater

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  1. Nick Chater
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Correspondence to Nick Chater.

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Chater, N. The logic of human learning. Nature 407, 572–573 (2000). https://doi.org/10.1038/35036662

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