A possible world semantics for disjunctive databases

The fundamental problem that arises when a ground atom in a disjunctive database is assumed false is discussed. There are basically two different approaches for inferring negative information for disjunctive databases: J. Minker´s (1982) generalized closed world assumption (GCWA) and K.A. Ross and R.W. Topor´s (1988) disjunctive database rule (DDR). It is argued that neither approach is satisfactory. A database semantics called PWS is proposed. It is shown that for propositional databases with no negative clauses, the problem of determining if a negative ground literal is inferred under the GCWA is co-NP-hard, while the same problem can be solved efficiently under the DDR and PWS. However, in the general case, the problem becomes co-NP-complete for the DDR and PWS. Relationships among GCWA, DDR, and PWS are highlighted. In general, disjunctive clauses are interpreted inclusively under the DDR and unpredictably under the GCWA