The Foundation of Typicality in the Similarity Structure of Natural Kinds

Milovanović, G. & Janković, D. (2008). The Foundation of Typicality in the Similarity Structure of Natural Kinds. XIV Conference “Empirical Research in Psychology”, 7. – 8. February, 2008. Faculty of Philosophy, University of Belgrade.

In the scope of the Categorical Theory of Similarity (CTS) the intra-categorical status of any concept is defined by the characteristics of the respective distribution of similarity between that concept and all other exemplars in the same category. Typicality is defined as degree to which a particular concept encodes the complexity of the category structure by its distribution of similarity toward other exemplars. For example, imagine that you have the task to explain what Birds are and chose to start by presenting an ostrich, and that the explanation of other concepts in the category proceeds by merely describing how your first exemplar is similar to the remaining ones. Obviously, an ostrich would not be very useful in this task, since most of the birds are different from it, and thus it has a low-informative distribution of similarity. Again, a pigeon could be a better solution to start with, since not only that many birds are similar to it, but there are also birds that differ from it; this concepts encodes more complexity in the intra-categorical structure of similarity in the category of Birds. Following this logic, we introduce simple mathematical hypothesis about the shape of the distribution of similarity, constraining it to have correlated mean, variance and entropy, so that the more typical exemplars (having higher means on the typicality scale) also have a more developed similarity structure encoded by the respective distribution. The model of the distribution of similarity is based on a Bayesian inference on the Poisson distribution (using a non-informative Gamma as a conjugate prior) and it satisfies the above mentioned characteristics:

• if a discrete inter-concept similarity measure (originating from an Likert scale, for example) of a single concept follows the Poisson distribution,

• with a rate parameter λ and index k, and taking λ to have a non-informative prior Gamma distribution with shape parameter α→0 and inverse scale parameter β→0, iteratively adding all measurements from the respective scale we infer a posterior λ ~ Gamma(α’, β’), taking its modal value (the MAP estimate) to be a final estimate of the rate parameter of the distribution of similarity for a particular concept.

We predict that the this final estimate will be able to predict the respective typicality measure.

Materials used to test the model were verbal stimuli encompassing 20 concepts from each of six natural kinds: Mammals, Birds, Insects, Cities, Rivers and Mountains. The typicality data for all stimuli were collected in a scaling experiment with 20 Ss rating the typicality of each of 120 concepts on 5-point scales. The application of the described model on similarity data (drawn from similarity norms for Serbian, Milovanović, 2004) shoes how the values of posterior λ parameters succesfully predict typicality ratings, with significant values R² values of .85 (mammals), .78 (birds), .24 (Insects), .85 (Mountains), .76 (Cities) and .82 (Rivers). Compared to similar models of typicality (cf. Storms, De Boeck & Ruts, 2000) , the modeling approach based on CTS performs with comparable or better success in predicting typicality measures based on a fairly simple and yet fundamental approach.