Total unbiased multivalued paraconsistent semantics of database integrity

A total semantics of integrity is defined for all databases. An unbiased semantics is one which does not take sides with regard to the satisfaction or violation of constraints. A multivalued semantics accommodates more than two truth values. A paraconsistent semantics is one which does not invalidate integrity evaluation in the presence of inconsistency. We define and discuss a total unbiased three-valued semantics of database integrity and a four-valued refinement thereof. Each of the presented semantics is paraconsistent in the sense that they tolerate inconsistent integrity theories.