A Possibilistic Assumption-Based Truth Maintenance System with Uncertain Justifications, and its Application to Belief Revision

possibilistic model, both changes of weights or labels lead to almost no more computations than in De Kleer's original model. Lastly, the other models cannot handle disjunctions of assumptions ; besides, Provan's model needs to consider the assumptions as independent as long as they are not mutually exclusive (i.e. not containing any nogood). Possibilistic ATMS do not require this assumption, and can handle disjunctions of assumptions, as well as negated assumptions. In summary, possibilistic ATMS proposes a joint handling of assumptions and uncertainty relative to a knowledge base, in the framework of possibilistic logic, by ordering the environments of a proposition according to the certainty with which it can be deduced from each of them. The fact that possibilistic logic remains on many points close to classical logic facilitates the extension of efficient procedures, such as those based on CAT-correct resolution for the computation of labels, nogoods and contexts. Possibilistic ATMS can be applied to truth maintenance problems in presence of uncertainty, to default reasoning, to fault diagnosis (see [9]), or to generation of (the most plausible) explanations. Acknowledgements : The authors would like to thank Michel Cayrol and Pierre Tayrac for many fruitful discussions about ATMS and CAT-correct resolution. The approach presented in this paper differs from the ones mentioned in the introduction and which handle uncertainty, on several points : First, the ATMS with embedded belief functions enable us to rank interpretations (i.e. maximal consistent environments), as they intend to do, but they cannot handle the uncertainty pervading the knowledge base if any, i.e. the justifications. They hold the justifications as classical knowledge (i.e. certain) and, putting weights on the assumptions, they deduce the weights attached to the other propositions. Our approach does not attach any a priori weight to each proposition (assumptions or non-assumptions) but assigns a certainty degree to the clauses contained in the knowledge base (not only justifications, but also disjunctions of assumptions and nogoods specified by the user) ; then, taking into account this uncertain knowledge, we establish a mapping from certainty degrees assigned to assumptions to the certainty degrees of the propositions (i.e. the consequences of the assignment). Secondly, in the other approaches, truth maintenance and uncertainty management are completely separated, i.e. the label of a proposition p is first computed, then Bel(p) is computed (of course, taking into account Label(p)). Our approach completely integrates the uncertainty management into the truth maintenance system, …