ABSTRACT
The study of the semantics of logic programs rests on a certain amount of order theory and logic. This chapter discusses certain important and well-known fixed-point theorems applying to functions defined on ordered sets. In fact, the first of these theorems has fundamental applications in the semantics of computation in general, as well as in logic programming semantics. Many aspects of theoretical computer science depend on the notion of a partially ordered set. More structure is often required, however, than is provided simply by a partial order or even by a complete partial order or complete lattice. Mathematically speaking, the denotational semantics, or mathematical semantics, approach to the theory of procedural and functional programming languages is highly involved with providing a satisfactory framework within which to model constructs made in conventional programming languages. Fixed points of certain operators associated with logic programs are of extreme importance in the semantics of logic programs.
