Partial semantics for disjunctive deductive databases

We consider in this paper interesting subclasses of partial stable models which reduce the degree of undefinedness, namely M-stable (Maximal-stable) models, which coincide with regular models, preferred extension, and maximal stable classes, and L-stable (Least undefined-stable) models, and we extend them from normal to disjunctive deductive databases. L-stable models are shown to be the natural relaxation of the notion of total stable model; on the other hand the less strict M-stable models, endowed with a modularity property, may be appealing from the programming and computational point of view. M-stable and L-stable models are also compared with regular models on disjunctive deductive databases. it appears that, unlike on normal deductive databases, M-stable models do not coincide with regular models. Moreover, both M-stable and L-stable models satisfy the CWA principle, while regular models do not.