The engineering advances started in the second half of the 20th century have created an avalanche of new technology. Control and use of that technology require, among many things, effective computational methods for logic. This book proposes one such method. It makes use of a theory of logic computation based on matroid theory, in particular matroid decomposition. Main features of the theory are an extension of propositional logic, an analysis of logic formulas via combinatorial structures, and a construction of logic solution algorithms based on that analysis. The results have been implemented in a software system for logic programming called the Leibniz System.