Recently, the logics of minimal knowledge and negation as failure MKNF  was used to introduce hybrid MKNF knowledge bases , a powerful formalism for combining open and closed world reasoning for the Semantic Web. We present an extension based on a new three-valued framework including an alternating fixpoint, the well-founded MKNF model. This approach, the well-founded MKNF semantics, derives its name from the very close relation to the corresponding semantics known from logic programming. We show that the well-founded MKNF model is the least model among all (three-valued) MKNF models, thus soundly approximating also the two-valued MKNF models from . Furthermore, its computation yields better complexity results (up to polynomial) than the original semantics where models usually have to be guessed.
Alferes, J. J.,
& Hitzler, P.
(2007). Towards Tractable Local Closed World Reasoning for the Semantic Web. Lecture Notes in Computer Science, 4874, 3-14.