ABSTRACT
This chapter studies supported models in two-valued and three-valued logic, and applies generalized metric fixed-point theorems in order to show that certain classes of programs are uniquely determined. More general fixed-point theorems allow the treatment of more general classes of programs, so that the hierarchy of fixed-point theorems gives rise to a hierarchy of program classes, each of which has the property that all programs in the class have unique supported models. Such program classes are consequently called unique supported model classes. The chapter establishes a correspondence between semantics defined, on the one hand, by means of monotonic operators, and characterizations given by means of level mappings, on the other hand. Application of the Banach contraction mapping theorem can be replaced by application of Matthews’ theorem when passing from acyclic to acceptable programs. The chapter studies the variants of the Fitting operator and relates them to the classes of programs.
