On approximation of the semantic operators determined by bilattice-based logic programs

Abstract. We introduce the class of bilattice-based annotated logic programs (BAPs). These programs extend the general annotated programs of Kifer and Subrahmanian to the bilattice case. The immediate consequence operator TP is defined for BAPs and its continuity is proven. A theorem of Seda concerning the approximation of the least fixed point of the two-valued TP-operator is generalized to the case of BAPs. Finally, alternative bilattice-based logic programs are compared with BAPs, and theorems on the computation of the least fixed points of their semantic operators are established. This gives an extension of the theorem on approximation of the least fixed point of TP to a wide class of bilattice-based logic programs.