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Proof Theory for XPath using Hybrid Logic tools

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 Raul Fervari
Le mardi 11 juillet 2017 à 11:00
Salle de Conférence (Pavillon des Jardins)
Raul Fervari (FaMAF-Universidad Nacional de Córdoba, and CONICET, Argentina)

XPath is arguably the most widely used XML query language. It is fundamentally a general purpose language for addressing, searching, and matching pieces of an XML document. The navigational fragment of XPath, known as Core-XPath is essentially a modal logic, since it allows us to describe structural properties of relational models, i.e., of XML documents (see e.g. [1]). However, without the ability to relate nodes based on the actual data values of the attributes, the logic’s expressive power is inappropriate for many applications. The extension of Core-XPath with (in)equality tests between attributes of elements in an XML document, named Core-Data-XPath (here XPath=) is more appropriate in some of these situations. Recent articles also investigate XPath= from a modal perspective.

In this talk I will start by motivating the use of XPath=. Then we will discuss proof systems for XPath=, and will present and motivate our approach. The main idea is that we extend XPath= with nominals and the hybrid operator @ to take advantage of tools used in proof theory for Hybrid Logic. We focus in the definition of an Hilbert-style axiomatic system [2] for this logic, whose completeness proof is based in a Henkin-style construction. Finally we will discuss a similar idea for defining a terminating tableaux calculus for the same logic [3], before concluding with future directions.

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