Three types of redundancy in integrity checking: An optimal solution

Known methods for checking integrity constraints in deductive databases do not eliminate all aspects of redundancy in integrity checking. By making the redundancy aspects of integrity constraint checking explicit, independently from any chosen method, it is possible to develop a new method that is optimal with respect to the classiied redundancy aspects. We distinguish three types of redundancy and propose an integrity checking method based on revised inconsistency rules. A deductive database consists of facts, rules and inconsistency indicators. Facts are ground atoms of the form p(c 1 ; : : : ; c n) where p is an n-ary predicate symbol and c 1 ; : : : ; c n are (individual) constants. A rule is a clausal form expression of the form H 1 where each H i ; B j and A l is an atomic formula. For reasons of simplicity of presentation we restrict ourselves to rules with k = 1 and n = 0. An integrity constraint is a universally quantiied closed rst-order formula. And an inconsistency indicator is the negation of an integrity constraint.