  Initially introduced by Peter Hammer, Logical Analysis of Data is a
methodology that aims at computing a logical justification for dividing a group
of data in two groups of observations, usually called the positive and negative
groups. Consider this partition into positive and negative groups as the
description of a partially defined Boolean function; the data is then processed
to identify a subset of attributes, whose values may be used to characterize
the observations of the positive groups against those of the negative group.
  LAD constitutes an interesting rule-based learning alternative to classic
statistical learning techniques and has many practical applications.
Nevertheless, the computation of group characterization may be costly,
depending on the properties of the data instances. A major aim of our work is
to provide effective tools for speeding up the computations, by computing some
\emph{a priori} probability that a given set of attributes does characterize
the positive and negative groups. To this effect, we propose several models for
representing the data set of observations, according to the information we have
on it. These models, and the probabilities they allow us to compute, are also
helpful for quickly assessing some properties of the real data at hand;
furthermore they may help us to better analyze and understand the computational
difficulties encountered by solving methods.
  Once our models have been established, the mathematical tools for computing
probabilities come from Analytic Combinatorics. They allow us to express the
desired probabilities as ratios of generating functions coefficients, which
then provide a quick computation of their numerical values. A further,
long-range goal of this paper is to show that the methods of Analytic
Combinatorics can help in analyzing the performance of various algorithms in
LAD and related fields.
