Preference dependency grammar (PDG) is a framework for integrating morphological, syntactic, and semantic analyses. PDG provides packed shared data structures that can efficiently encompass all possible interpretations at each level of sentence analyses with preference scores. Using the structure, PDG can calculate a globally optimized interpretation for the target sentence. This paper first gives an overview of the PDG framework by describing the base model of PDG, which is a sentence analysis model, called a "multi-level packed shared data connection model." Then this paper describes packed shared data structures, e.g., headed parse forests and dependency forests, adopted in PDG. Finally, the completeness and soundness of the mapping between the parse forest and the dependency forest are revealed.