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This paper describes a semantic basis for a compositional approach to the analysis of logic programs. A logic program is viewed as consisting of a set of modules, each module defining a subset of the program's predicates. Analyses are constructed by considering abstract interpretations of a compositional semantics. The abstract meaning of a module corresponds to its analysis and composition of abstract meanings corresponds to composition of analyses. Such an approach is essential for large program development so that altering one module does not require re-analysis of the entire program. We claim that for a substantial class of programs, compositional analyses which are based on a notion of abstract unfolding provide the same precision as non-compositional analysis. A compositional analysis for ground dependencies is included to illustrate the approach. To the best of our knowledge this is the first account of a compositional framework for the analysis of logic programs.