We consider rather general operators mapping valuations to (sets of) valuations in the context of the semantics of logic programming languages. This notion generalizes several of the standard operators encountered in this subject and is inspired by earlier work of M.C. Fitting. The fixed points of such operators play a fundamental role in logic programming semantics by providing standard models of logic programs and also in determining the computability properties of these standard models. We discuss some of our recent work employing topological ideas, in conjunction with order theory, to establish methods by which one can find the fixed points of the operators arising in logic programming semantics.
Seda, A. K.,
& Hitzler, P.
(2001). Semantic Operators and Fixed-Point Theory in Logic Programming. Proceedings of the 7th International Conference on Information Systems Analysis and Synthesis, 224-229.