A Revision of Dependency-Directed Backtracking for JTMS

Current algorithms for Dependency-Directed Backtracking (DDB) suffer from several limitations. The added justifications produced by Doyle's DDB are sufficient but are neither safe nor complete. Petrie's DDB solves this problem, but it can lead to cases where odd loops are introduced later into JTMS network by new justifications, and so can sometimes miss legitimate admissible labelings. Moreover, Petrie's DDB cannot resolve an inconsistency if all possible added justifications produce an odd loop, although a solution may exist. We propose a revised method based on elective sets and premise sets of contradiction foundations that allows to use the premises as added justifications. Our revised DDB allows to resolve more inconsistencies than Petrie's DDB. Moreover, a preference ordering over the assumption justifications can be integrated; this order gives the problem solver some control over the choice of electives.