A LOGICAL CHARACTERIZATION FOR TRUTH MAINTENANCE SYSTEMS WITH DEPENDENCY‐DIRECTED BACKTRACKING

In this paper we present various logical characterizations of justification‐based (nonmonotonic) truth maintenance systems (JTMS). These characterizations, which are proved to be equivalent, aim at describing dependency‐directed backtracking (DDB) (i.e., the process of resolving conflicts which can arise when nogoods are allowed in the set of justifications), mainly relying on the intuitive idea that a contrapositrve use of justifications is needed to resolve inconsistencies. The idea is first formalized by means of the notion of three‐valued labeling and then through a transformation which explicitly adds all contrapositives of the justifications. An abductive characterization of the JTMS is provided through a further transformation which converts a set of nonmonotonic justifications to a corresponding abduction framework. This approach provides a unifying framework, based on the notion of abduction, for describing both JTMSs and assumption‐based TMSs (ATMSs).