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A major challenge of query language design is the combination of expressivity with effective static analyses such as query containment. In the setting of XML, documents are seen as finite trees, whose structure may additionally be constrained by type constraints such as those described by an XML schema. We consider the problem of query containment in the… (More)

We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of a given node. By contrast, the logic introduced in the present work can concisely express numerical bounds on any… (More)

We study the analysis problem of XPath expressions with counting constraints. Such expressions are commonly used in document transformations or programs in which they select portions of documents subject to transformations. We explore how recent results on the static analysis of navigational aspects of XPath can be extended to counting constraints. The… (More)

Regular path expressions represent the navigation core of the XPath query language for semi-structured data (XML), and it has been characterized as the First Order Logic with Two Variables (FO 2). Data tests refers to (dis)equality comparisons on data tree models, which are unranked trees with two kinds of labels, propositions from a finite alphabet, and… (More)

Modal logics forms a family of formalisms widely used as reasoning frameworks in diverse areas of computer science. Description logics and their application to the web semantic is a notable example. Also, description logics have been recently used as a reasoning model for context-aware systems. Most reasoning algorithms for modal (description) logics are… (More)