Learning the semantics of discrete random variables: Ordinal or categorical

When specifying a probabilistic model of data, the form of the model will typically depend on the spaces in which random variables take their values. In particular, different probability distributions are appropriate for continuous, discrete and binary data. As we respond to ever increasing quantities of data, with increasingly more automatic data analysis techniques, it is necessary to identify these different types of data automatically. While it is trivial to create concise logical rules to distinguish between many different types of data, this cannot be said for choosing between categorical and ordinal data, let alone inferring the ordering. We present some first attempts at this problem and evaluate their performance empirically.