A new representation of JTMS

A Justification -based Truth Maintenance System (JTMS) is classically represented by a network of nodes together with a set of links (justifications) that represent dependencies between nodes. In this representation, the relations between the justifications are not explicit. We propose a dual representation of a JTMS based on the dependencies between justifications. This representation allows us to separate the monotonic and non-monotonic parts of the network of dependencies. Based on this representation, we develop an incremental backtracking algorithm to compute an admissible labeling of a JTMS. This algorithm allows us to go from an admissible labeling to another, and so it always finds an admissible labeling when one exists, and dependency-directed backtracking must be called uniquely when all the admissible labelings are inconsistent.