Relativized Hyper equivalence of Logic Programs for Modular Programming

A recent framework of relativized hyper equivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows one to restrict, independently of each other, the head and body alphabets in context programs. The authors study relativized hyper equivalence for the three semantics of logic programs given by stable, supported and supported minimal models. For each semantics, they identify four types of contexts, depending on whether the head and body alphabets are given directly or as the complement of a given set. Hyper equivalence relative to contexts where the head and body alphabets are specified directly has been studied before.