A Three Valued Truth Maintenance System.
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TL;DR
In this paper a new approach is taken to truth maintenance algorithms that can be used to deduce the negation of antecedents that would lead to contradictions.
Abstract
Truth maintenance systems have been used in recently developed problem solving systems. A truth maintenance system (TMS) is designed to be used by deductive systems to maintain the logical relations among the beliefs which those systems manipulate. These relations are used to incrementally modify the belief structure when premises are changed, giving a more flexible context mechanism than has been present in earlier artificial intelligence systems. The relations among beliefs can also be used to directly trace the source of contradictions or failures, resulting in far more efficient backtracking.