On Equivalence of Queries Using Views

In this paper we consider views expressed as unions of conjunctive formulas, where predicates of literals are views or database relations. The negation is allowed in the body of views. We assume that the variables occurring in the head of a view also occur in this body. Moreover, in case all variables occurring in negated atoms also occur in positive ones, then that query is said to be with safe negated subgoals(the safeness property). A query has a similar form to that of a view. Queries and views are considered in conjunctive forms as a conjunction of literals, as well in disjunctive forms as union of queries in conjunctive forms, respectively. Given a view V and a database D, the materialization of V for D, denoted V(D), is defined. Also for a query Q and a database D, the answer of Q for D is defined. The expansion of a query Q using a view V denoted Expansion(Q, V) is defined. We study some conditions imposed on view V to ensure the equivalence between Q and Expansion(Q, V). In this paper we consider views and queries without the safeness property.