Meta many-valued logic programming for incomplete and locally inconsistent databases

We present a 2-valued logic obtained by ontological encapsulation of many-valued logic programming, for data integration of different source databases which can be incomplete and inconsistent. This new approach introduces the trilattice of interpretations with the new meta-truth dimension. We defined a model theoretic approach for Herbrand interpretations of an encapsulated logic program: they constitute a complete semilattice under knowledge preorder, so that is possible to apply the Knaster-Tarski theorem for monotonic ´immediate consequence operator´ in order to define the least fixpoint semantics for encapsulated logic programs, that is a unique 4-valued Herbrand model for databases.