Recovery of (non)monotonic theories

摘要

Recovery of a theory T is needed if it does not have a model under the given semantics Sem, i.e., if the theory is Sem-inconsistent. In general, to recover an inconsistent theory T, a transformation R is applied to T and T is replaced by a consistent theory R(T). If a classical semantics is used, it is clear that R should be a contraction. For nonmonotonic theories, e.g., nonmonotonic databases, however, in general it is unclear how to restore the consistency of such a theory: indeed, several options for recovery that use (mixtures of) contractions and expansions have been proposed in the literature. In this paper, we propose a more fundamental approach to study the recovery problem by stating some minimal set of rationality postulates for recovery. In these postulates we assume that, when recovering a theory T with respect to some intended semantics, one can fall back on a weaker, so called backup semantics for T. Based on these rationality postulates our general conclusion is that for cumulative theories, expansions are not suitable, while for noncumulative theories like default logic, auto-epistemic logic and nonmonotonic logic programming, contractions cannot be used as recovery operators.