$\exists$-universal termination of logic programs

We introduce the notion of $\exists$-universal termination of logic programs. A program P and a goal G $\exists$-universally terminate iff there exists a selection rule S such that every SLD-derivation of P U { G }$via S is finite. We claim that it is an essential concept for declarative programming, where a crucial point is to associate a terminating control strategy to programs and goals. We show that $\exists$-universal termination and universal termination via fair selection rules coincide. Then we offer a characterization of $\exists$-universal termination by defining fair-bounded programs and goals. They provide us with a correct and complete method of proving $\exists$-universal termination. We show other valuable properties of fair-bounded programs and goals, including persistency, modularity, ease of use in paper & pencil proofs, automatization of proofs.