We define a semantic framework to reason about properties of abstractions of SLD-derivations. The framework allows us to address problems such as the relation between the (top-down) operational semantics and the (bottom-up) denotational. semantics, the existence of a denotation for a set of definite clauses and their properties (compositionality w.r.t. various syntactic operators, correctness, minimality, and precision). Using abstract interpretation techniques to model abstraction allows us to state very simple conditions on the observables which guarantee the validity of several general theorems. (C) 2001 Academic Press.
