Structural characterizations of the navigational expressiveness of relation algebras on a tree

•Natural variations of Tarski's classic relation algebra are studied on trees.•The notion of instance expressibility is introduced and studied for these languages.•A robust methodology is given and used for characterizing instance expressivity.•Our characterizations are given for both global and local views on query semantics.•These characterizations are effectively computable and hence can be used in practice.

We study the expressiveness on a given document of various fragments of XPath, the core navigational language on XML documents. Viewing these languages as fragments of Tarski's relation algebra, we give characterizations for when a binary relation on the document's nodes (i.e., a set of paths) is definable by an expression in these algebras. In contrast with this “global view” on language semantics, there is also a “local view” where one is interested in the nodes to which one can navigate starting from a particular node. In this view, we characterize when a set of nodes can be defined as the result of applying an expression to a given node. All of these global and local definability results are obtained using a two-step methodology, which consists of first characterizing when two nodes cannot be distinguished by an expression in the language, and then bootstrapping these characterizations to the desired results.