A Transformation of Propositional Prolog Programs into Classical Logic

We transform a propositional Prolog program P into a set of propositional formulas prl(P ) and show that Prolog, using its depth-first left-to-right search, is sound and complete with respect to prl(P ). This means that a goal succeeds in Prolog if and only if it follows from prl(P ) in classical propositional logic. The generalization of prl(P ) to predicate logic leads to a system for which Prolog is still sound but unfortunately not complete. If one changes, however, the definition of the termination operator, then one obtains a theory that allows to prove termination of arbitrary non-floundering goals under Prolog.