"Optimal" Collecting Semantics for Analysis in a Hierarchy of Logic Program Semantics

In this paper we apply abstract interpretation to systematically derive, compose and compare semantics according to their expressive power. The main results are: (1) a definition of a hierarchy of collecting semantics, including well known semantics for logic programs, where semantics can be related to each other by abstract interpretation; (2) a characterization of collecting and abstract semantics in terms of collecting and abstract models for a program; (3) a correspondence between collecting and abstract models providing a ``logical'' interpretation of the typical loss of precision of abstract interpretation-based analysis; (4) a systematic approach to derive and compose collecting semantics in a lattice-theoretic environment; (5) a constructive characterization for the ``best'' collecting semantics for analysis.