On the existence of effective Hoare logics

Every proof system for (partial) correctness yields an enumeration procedure for correctness assertions. Other researchers have proved results on the existence of (sound and complete) enumeration procedures for assertions about programs from an acceptable programming language where the assertion language is first-order logic. It is shown that some of the assumptions are stronger than necessary, whereas others must not be weakened. Two novel procedures are given that work for more interpretations with a smaller oracle than those known up to now.