Many procedurally-oriented problem solving systems can be viewed as performing a mixture of computation and deduction, with much of the computation serving to decide what deductions should be made. This results in bits and pieces of deductions being strewn throughout the program text and execution. This paper describes a problem solver subsystem called a truth maintenance system which collects and maintains these bits of deductions. Automatic functions of the truth maintenance system then use these pieces of "proofs" to consistently update a data base of program beliefs and to perform a powerful form of backtracking called dependency-directed backtracking.
