A Possible World Semantics for Disjunctive Databases

We investigate the fundamental problem of when a ground atom in a disjunctive database is assumed false. There are basically two diierent approaches for inferring negative information for disjunctive databases; they are Minker's Generalized Closed World Assumption (GCWA) and Ross and Topor's Disjunctive Database Rule (DDR). A problem with the GCWA is that disjunctive clauses are sometimes interpreted exclusively, even when they are intended for inclusive interpretation. On the other hand, the DDR always interprets disjunctive clauses inclusively. We argue that neither approach is satisfactory. Whether a disjunctive clause is interpreted exclusively or inclusively should be speciied explicitly. Negative information should then be inferred according to the stated intent of the disjunctive clauses. A database semantics called PWS is proposed to solve the aforementioned problem. We also show 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 eeciently 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. We also characterize when the GCWA interprets disjunctive clauses exclusively. Throughout this discussion, we assume both the head and the body of a clause consist of atoms only.