Minimalism, justification and non-monotonicity in deductive databases

Abstract

Three formalizations of the closed world assumption (CWA) which accomodate disjunctive information are compared. The semantic approach of Bossu and Siegel, here called “minimalism,” is shown to be equivalent to the syntactic approach based on Reiter's “default logic,” when a specific class of defaults corresponding to the CWA is used. Neither approach generalizes the “negation as failure” (NAF) inference rule of Clark. The three formalizations are synthesized to form “positivism,” a new semantically defined formalization of the CWA. The expressive power of minimalism and positivism is compared, in both static and dynamic contexts. In the dynamic case the comparison shows that positivism and minimalism are “non-monotonic” in different ways. Finally, positivism and “stratification,” an alternative formalization of the CWA which combines minimalism and NAF are briefly compared.