A new algorithm for truth maintenance

The author offers a truth maintenance algorithm which combines key features of existing algorithms. Like J. de Kleer´s (1986) ATMS (assumption-based truth maintenance systems), it finds all solution states of belief and avoids dependency-directed backtracking. Like J. Doyle´s (1979) TMS, it deals explicitly with nonmonotonic justifications and arguments for beliefs. The algorithm uses a novel representation for sets of belief states which focuses on certain regularities in the space of TMS solutions. Preliminary experiments show that, although its time complexity is theoretically exponential, the algorithm performs well on a moderate-size problem (~100 beliefs) which displays the appropriate regularity. As expected, exponential behavior is seen in the n-queens and bit parity problems, which have large solution spaces lacking the required regularity. To address the complexity problem, it appears feasible to modify the algorithm to compute partial sets of solutions