Experimental data is often given as bit vectors, with vectors corresponding to observations, and coordinates to attributes, with a bit being true if the corresponding attribute was observed. Observations are usually grouped, e.g. into positive and negative samples. Among the essential tasks on such data, we have compression, the construction of classifiers for assigning new data, and information extraction. Our system, MCP, approaches these tasks by propositional logic. For each group of observations, MCP constructs a (usually small) conjunctive formula that is true for the observations of the group, and false for the others. Depending on the settings, the formula consists of Horn, dual-Horn, bijunctive or general clauses. To reduce its size, only relevant subsets of the attributes are considered. The formula is a (lossy) representation of the original data and generalizes the observations, as it is usually satisfied by more bit vectors than just the observations. It thus may serve as a classifier for new data. Moreover, (dual-)Horn clauses, when read as if-then rules, make dependencies between attributes explicit. They can be regarded as an explanation for classification decisions.