Domain-general categorisation explains constrained cross-linguistic variation in noun classification

This file formalizes the two formal claims of Prasertsom, Smith and Culbertson. The paper asks why animacy, but never colour, serves as a basis for noun classification although both are perceptually salient, and answers with a domain-general principle: a good category is one whose defining feature predicts the other features of its members, and animacy predicts more than colour. The typological premise is read off Aikhenvald's sample of noun categorization devices, where animacy is a basic semantic parameter and colour is none of any device's (animacy_not_colour). The predictive-power manipulation of Experiments 3a and 3b rests on two sixteen-stimulus sets, Tables 4 and 5 (predictiveAnimacy, predictiveColour), built so that the conditional entropy of horn type, body shape, and appendage shape is lower given the predictive dimension than given the other, and so that exchanging the animacy and colour columns of one set gives the other (mirror_images). The six entropy orderings of Table 6 that the design promises are proved from the tables under the uniform measure over the stimuli (predictiveAnimacy_horn, predictiveColour_horn, and their shape and appendage siblings).

Implementation notes

Each stimulus set has exactly one stimulus per animacy–colour pair, so a set is a function from the pair to the three remaining dimensions and its stimuli are the sixteen cells of the grid. Conditional entropy is the substrate's H[X | Y ; μ] under the uniform measure on the grid, reduced to counts by condEntropy_uniformOn_univ; each ordering then comes to a positive multiple of negMulLog (1/2), the entropy of the evenly split fibres that only the non-predictive dimension has. The learning and sorting results of Experiments 1a to 3b and the corpus measures of §4.1, which are means over participants and word embeddings, are not formalized.

TODO

The paper's reason for the mirror design, that animacy in one set has exactly the predictive power of colour in the other, is the invariance of conditional entropy under a relabelling of the population and of the conditioning variable; the substrate has no such lemma yet, so the predictive-colour orderings are computed directly rather than transferred from the predictive-animacy ones through mirror_images.

References

• Prasertsom et al. 2026, Domain-general categorisation explains constrained cross-linguistic variation in noun classification
• Aikhenvald 2000, Classifiers: A Typology of Noun Categorization Devices formalized