Fully abstract compositional semantics for logic programs

The authors propose a framework for discussing fully abstract compositional semantics, which exposes the interrelations between the choices of observables, compositions, and meanings. Every choice of observables and compositions determines a unique fully abstract equivalence. A semantics is fully abstract if it induces this equivalence. They study the semantics of logic programs within this framework. They find the classical Herbrand-base semantics of logic programs inadequate, since it identifies programs that should be distinguished and vice versa. They therefore propose alternative semantics, and consider the cases of no compositions, composition by program union, and composition of logic modules (programs with designated exported and imported predicates). The authors prove that their fully abstract semantics are always in a subvocabulary of that of the program. This subvocabulary, called the essential vocabulary, is common to all equivalent programs.