  We investigate explainability via short Boolean formulas in the data model
based on unary relations. As an explanation of length k, we take a Boolean
formula of length k that minimizes the error with respect to the target
attribute to be explained. We first provide novel quantitative bounds for the
expected error in this scenario. We then also demonstrate how the setting works
in practice by studying three concrete data sets. In each case, we calculate
explanation formulas of different lengths using an encoding in Answer Set
Programming. The most accurate formulas we obtain achieve errors similar to
other methods on the same data sets. However, due to overfitting, these
formulas are not necessarily ideal explanations, so we use cross validation to
identify a suitable length for explanations. By limiting to shorter formulas,
we obtain explanations that avoid overfitting but are still reasonably accurate
and also, importantly, human interpretable.
