PDL for ordered trees

Afanasiev, Loredana; Blackburn, Patrick; Dimitriou, Ioanna M.; Gaiffe, Bertrand; Goris, Evan; Marx, Maarten; Rijke, Maarten de

doi:10.3166/jancl.15.115-135

Cited by 43 publications

(61 citation statements)

References 12 publications

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“…By reducing it to the original result, [2] show that the same complexity holds for the logic of trees.…”

Section: Theorem 10 ([22])mentioning

confidence: 98%

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Modal Logic Foundations of Markup Structures in Annotation Systems

Kracht

2011

Modeling, Learning, and Processing of Text Technological Data Structures

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“…By reducing it to the original result, [2] show that the same complexity holds for the logic of trees.…”

Section: Theorem 10 ([22])mentioning

confidence: 98%

“…XPath is a language that allows to define and use relations in a document. XPath is most directly connected with modal logic (see [2]). Research has therefore proceeded by comparing XPath with various variants of modal logic.…”

Section: Introductionmentioning

confidence: 99%

Modal Logic Foundations of Markup Structures in Annotation Systems

Kracht

2011

Modeling, Learning, and Processing of Text Technological Data Structures

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“…However, regular tree languages are not fully captured by such FO variants (Benedikt and Segoufin, 2005). The work found in (Afanasiev et al, 2005) proposes a variant of Propositional Dynamic Logic (PDL) (Fischer and Ladner, 1979) with a similar EXPTIME complexity for reasoning about ordered trees, but whose exact expressive power is still under study.…”

Section: Related Workmentioning

confidence: 99%

Deciding XPath containment with MSO

Genevès¹,

Layaïda²

2007

Data & Knowledge Engineering

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XPath is the standard language for addressing parts of an XML document. We present a sound and complete decision procedure for containment of XPath queries. The considered XPath fragment covers most of the language features used in practice. Specifically, we show how XPath queries can be translated into equivalent formulas in monadic second-order logic. Using this translation, we construct an optimized logical formulation of the containment problem, which is decided using tree automata. When the containment relation does not hold between two XPath expressions, a counter-example XML tree is generated. We provide practical experiments that illustrate the efficiency of the decision procedure for realistic scenarios.

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“…The connection between XML navigation and temporal logics was best demonstrated in the work of Marx [25] and his followers [7,1,2,15]. In particular, [25] gave an expressive completeness result for XPath: adding a temporal until operator (found in logics such as LTL, CTL) to the core of XPath gives it precisely the power of FO, one of the yardstick database query languages.…”

Section: Introductionmentioning

confidence: 99%

Combining Temporal Logics for Querying XML Documents

Arenas

Barceló

Libkin

2006

Lecture Notes in Computer Science

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Abstract. Close relationships between XML navigation and temporal logics have been discovered recently, in particular between logics LTL and CTL and XPath navigation, and between the µ-calculus and navigation based on regular expressions. This opened up the possibility of bringing model-checking techniques into the field of XML, as documents are naturally represented as labeled transition systems. Most known results of this kind, however, are limited to Boolean or unary queries, which are not always sufficient for complex querying tasks. Here we present a technique for combining temporal logics to capture nary XML queries expressible in two yardstick languages: FO and MSO. We show that by adding simple terms to the language, and combining a temporal logic for words together with a temporal logic for unary tree queries, one obtains logics that select arbitrary tuples of elements, and can thus be used as building blocks in complex query languages. We present general results on the expressiveness of such temporal logics, study their model-checking properties, and relate them to some common XML querying tasks.

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PDL for ordered trees

Cited by 43 publications

References 12 publications

Modal Logic Foundations of Markup Structures in Annotation Systems

Modal Logic Foundations of Markup Structures in Annotation Systems

Deciding XPath containment with MSO

Combining Temporal Logics for Querying XML Documents

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