Positivism vs minimalism in deductive databases

Three formalizations of the Closed World Assumption (CWA) which accommodate disjunctive informaticn are compared. The semantic approach of Bossu and Siegel, here called *minimalismm, is shown to be equivalent to the syntact.ic approach based on Reiter’s ‘default. logic”, when a specific class of defaults corresponding to bhe CWA is used. Neit.her approach generalizes the ‘Negation as Failure’ inference rule of Clark. The t.hree formalizations are synthesized to form “positivism”, a new semantically-defined formalization of the CWA. The expressive power of minimalism a.nd positivism is compared, in both static and dynamic contexts. In the dynamic case the comparison shows that positivism an’d minimalism are “non-monotonic. in different ways.