Naive Bayesian classifiers are very successful in attribute-value representations. However, it is not clear how the decomposition of the probability distributions on attribute-value tuples underlying those classifiers can be applied on structured individuals, for instance sets of tuples as in the multiple instance problem. This paper presents a decomposition of probability distributions on structured individuals. It shows how it results in a propositionalisation of the data guided by the decomposition of the structure of the individual. This is illustrated by using the first-order naive Bayesian classifier 1BC to perform the decomposition of probability distributions on structured individuals.