A logical foundation for logic programming I. Biconsequence relations and nonmonotonic completion

We suggest a general logical formalism for Logic Programming based on a four-valued inference. We show that it forms a proper setting for representing logic programs with negation as failure of a most general kind and for describing logics and semantics that characterize their behavior. In this way we also extend the connection between Logic and Logic Programming beyond positive programs. In addition, the suggested formalism will allow us to see a reasoning about logic programs as a most simple kind of nonmonotonic reasoning in general. (C) 1998 Elsevier Science Inc. All rights reserved.