Structural characterizations of the semantics of XPath as navigation tool on a document

Abstract

Given a document D in the form of an unordered labeled tree, we study the expressibility on D of various fragments of XPath, the core navigational language on XML documents. We give characterizations, in terms of the structure of D, for when a binary relation on its nodes is definable by an XPath expression in these fragments. Since each pair of nodes in such a relation represents a unique path in D, our results therefore capture the sets of paths in D definable in XPath. We refer to this perspective on the semantics of XPath as the "global view." In contrast with this global view, there is also a "local view" where one is interested in the nodes to which one can navigate starting from a particular node in the document. In this view, we characterize when a set of nodes in D can be defined as the result of applying an XPath expression to a given node of D. All these definability results, both in the global and the local view, are obtained by using a robust two-step methodology, which consists of first characterizing when two nodes cannot be distinguished by an expression in the respective fragments of XPath, and then bootstrapping these characterizations to the desired results.

The impact of transitive closure on the expressiveness of navigational query languages on unlabeled graphs

“…However, it is possible that two fragments can be separated for general graphs but not for trees as input. Some results on the expressive power of XPath fragments (e.g., [6,9,14,19,20,26]) can readily be used for this purpose, but some relation algebra features do not straightforwardly correspond with XPath operations. Consequently, the results of this study will contribute to a better understanding of querying tree-shaped documents, in particular in the case where several documents are involved.…”

“…This study was motivated by similar work on the expressive power of XPath fragments as query languages for navigating on trees, which is now well understood (e.g., [6,9,14,19,20,26]). Motivated by data on the Web [1,12] and new applications such as dataspaces [13], Linked Data [7,16], and RDF [23], it is natural to look at similar navigational query languages for graphs.…”

Relative expressive power of downward fragments of navigational query languages on trees and chains

“…Lastly, the XPath algebra of Gyssens et al [12,15], when restricted to the downward fragment, corresponds to the navigational query language N (π, ∩, \), and the positive algebra of Wu et al [26], when restricted to the downward fragment, corresponds to the navigational query language N (π, ∩). Although these studies include some expressiveness results, these results are dependent on the availability of a parent-axis (or a converse operator), and, thus, these results are not relevant for our study.…”

“…Much less is known for the more restrictive tree data model, however: most of the results on graphs do not directly apply to trees. There are expressiveness results for several XPath fragments [3,12,15,19,20,23,24,26] in the context of XML, but these results do not provide a complete picture of the relative expressive power of the various fragments of the navigational query languages we consider here. As a first step towards this aim, we study the expressive power of the downward fragments: these are the navigational query languages that only allow downward navigations in the tree via parent-child relations.…”

On the Expressive Power of the Relational Algebra on Finite Sets of Relation Pairs

“…It may also prove fruitful to investigate similar generalizations of instance-driven query discovery for graph [5] and XML [7] data. We close by noting several further open questions which naturally arise from the present investigation.…”