Structural Properties of XPath Fragments

We study structural properties of each of the mainsublanguages of XPath [8] commonly used in practice.First, we characterize the expressive power of these lan-guage fragments in terms of both logics and tree pat-terns. Second, we investigate closure properties, fo-cusing on the ability to perform basic Boolean oper-ations while remaining within the fragment. We give acomplete picture of the closure properties of these frag-ments, treating XPath expressions both as functions ofarbitrary nodes in a document tree, and as functionsthat are applied only at the root of the tree. Finally,we provide sound and complete axiom systems and nor-mal forms for several of these fragments. These resultsare useful for simpli cation of XPath expressions andoptimization of XML queries.