There are many classifiers that treat entities to be classified as points in a high-dimensional vector space and then compute a separator S between entities in class +1 from those in class -1. However, such classifiers are usually very hard to explain in plain English to domain experts. We propose Metric Logic Programs (MLPs) which are a fragment of constraint logic programs as a new paradigm for explaining S. We present multiple measures of quality of an MLP and define the problem of finding an MLP-Explanation of S and show that it - and various related problems - are NP-hard. We present the MLP_Extract algorithm to extract MLP explanations for S. We show that while our algorithms provide more succinct, simpler, and higher fidelity explanations than association rules that are less expressive, our algorithms do require additional run-time.