A Truth Maintenance -System (TMS) maintains a consistent state of belief given a set\ud J of justifications, i.e. arguments for belief. To resolve contradictions dependency-directed backtracking is performed.\ud In this paper we introduce a method that can, be used to track all dependency-directed\ud backtracking methods simultaneously. This has been, previously done, by adding the contrapositions\ud of justifications to J. We will show that contrapositions are not mandatory, namely\ud that the same result can be reached by adding one disjunctive justification (the consequent is\ud not one atom, but can be a disjunction of atoms).\ud Simplifying the added disjunctive justification leads to more informative models [Ross 89b].\ud Furthermore, we will give an alternative proof for the correctness of Witteveen's method\ud [Witteveen 90a] for computing the Well-Founded mode
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