Corollaries on the fixpoint completion: studying the stable semantics by means of the Clark completion
Abstract
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 (1989). 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 (2002), 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.
Keywords
Cite
@article{arxiv.cs/0402013,
title = {Corollaries on the fixpoint completion: studying the stable semantics by means of the Clark completion},
author = {Pascal Hitzler},
journal= {arXiv preprint arXiv:cs/0402013},
year = {2007}
}
Comments
15 pages. Presented at the 18th Workshop on Logic Programming, Potsdam, Germany, March 2004