Corollaries on the Fixpoint Completion: Studying the Stable Semantics by Means of the Clark Completion

The fixpoint completion fix (P) of a normal logic program P is a program transformation such that the stable models of P are exactly the models of the Clark completion of fix (P). This is well-known and was studied by Dung and Kanchanasut [15]. The correspondence, however, goes much further: The Gelfond-Lifschitz operator of P coincides with the immediate consequence operator of fix (P), as shown by Wendt [51], and even carries over to standard operators used for characterizing the well-founded and the Kripke-Kleene semantics. We will apply this knowledge to the study of the stable semantics, and this will allow us to almost effortlessly derive new results concerning fixed-point and metric-based semantics, and neural-symbolic integration