A collection of techniques in artificial intelligence that records dependencies between assertions in a logical database. Given a query and a database, a truth-maintenance system will return a set of statements, called an explanation, that supports the query; hence the query statement can be derived from the statements in the explanation. Applications are found in diagnosis, where a complete model of the working system is used to reason from symptoms to causes; an explanation, generated by a fault query, defines the steps from symptoms to cause. This is different from heuristic rule-based systems and probabilistic systems, which mainly use reasoning rules that relate cause to symptom.