Characterizations of classes of programs by three-valued operators

Abstract

Several important classes of normal logic programs, including the classes of acyclic, acceptable, and locally hierarchical programs, have the property that every program in the class has a unique two-valued supported model. In this paper, we call such classes unique supported model classes. We analyse and characterize these classes by means of operators on three-valued logics. Our studies will motivate the definition of a larger unique supported model class which we call the class of Φ*-accessible programs. Finally, we show that the class of Φ*-accessible programs is computationally adequate in that every partial recursive function can be implemented by such a program.