The thesis developed here is that reasoning programs which take care to record the logical justifications for program beliefs can apply several powerful, but simple, domain-independent algorithms to (1) maintain the consistency of program beliefs, (2) realize substantial search efficiencies, and (3) automatically summarize explanations of program beliefs. These algorithms are the recorded justifications to maintain the consistency and well founded basis of the set of beliefs. The set of beliefs can be efficiently updated in an incremental manner when hypotheses are retracted and when new information is discovered. The recorded justifications also enable the pinpointing of exactly whose assumptions which support any particular belief. The ability to pinpoint the underlying assumptions is the basis for an extremely powerful domain-independent backtracking method. This method, called Dependency-Directed Backtracking, offers vastly improved performance over traditional backtracking algorithms.