PDL for ordered trees

@article{Afanasiev2005PDLFO,
  title={PDL for ordered trees},
  author={Loredana Afanasiev and Patrick Blackburn and Ioanna M. Dimitriou and Bertrand Gaiffe and Evan Goris and maarten marx and M. de Rijke},
  journal={Journal of Applied Non-Classical Logics},
  year={2005},
  volume={15},
  pages={115 - 135}
}
This paper is about a special version of PDL, proposed by Marcus Kracht, for reasoning about sibling ordered trees. It has four basic programs corresponding to the child, parent, left- and right-sibling relations in such trees. The original motivation for this language is rooted in the field of model-theoretic syntax. Motivated by recent developments in the area of semi-structured data, and, especially, in the field of query languages for XML (eXtensible Markup Language) documents, we revisit… 
Explorer Combining Temporal Logics for Querying XML Documents
TLDR
This work presents a technique for combining temporal logics to capture nary XML queries expressible in two yardstick languages: FO and MSO, and shows that by adding simple terms to the language, one obtains logics that select arbitrary tuples of elements, and can thus be used as building blocks in complex query languages.
Node Selection Query Languages for Trees
The study of node-selection query languages for (finite) trees has been a major topic in the recent research on query languages for Web documents. On one hand, there has been an extensive study of
Combining Temporal Logics for Querying XML Documents
TLDR
This work presents a technique for combining temporal logics to capture n-ary XML queries expressible in two yardstick languages: FO and MSO, and shows that by adding simple terms to the language, one obtains logics that select arbitrary tuples of elements, and can thus be used as building blocks in complex query languages.
A system for the static analysis of XPath
TLDR
This work proposes a unifying logic for XML, namely, the alternation-free modal μ-calculus with converse, and shows how to translate major XML concepts such as XPath and regular XML types (including DTDs) into this logic.
Comparing XML path expressions
TLDR
This paper proposes a logic-based framework for the static analysis of XPath and presents a translation of a large XPath fragment into μ-calculus, together with practical experiments on the containment using a state-of-the-art EXPTIME decision procedure for μ-Calculus satisfiability.
Logics for XML
TLDR
A new class of static analyzers for programs manipulating XML data allow to ensure at compile-time valuable properties such as type-safety and optimizations, for safer and more efficient XML processing.
Decidable XPath Fragments in the Real World
TLDR
This work designs a benchmark compiling thousands of real-world XPath queries extracted from open-source projects, and matches them against syntactic fragments from the literature, to investigate the practical impact of theoretical fragments of XPath.
Mu-Calculus Based Resolution of XPath Decision Problems
TLDR
This paper proposes a unifying logic for XML, namely the alternation-free modal mu-calculus with converse, and shows how to translate major XML concepts such as XPath and DTDs into this logic, as well as providing preliminary experiments which shed light, for the first time, on the cost of solving XPath decision problems in practice.
Efficient static analysis of XML paths and types
TLDR
An algorithm to solve XPath decision problems under regular tree type constraints and its use to statically type-check XPath queries is presented and the decidability of a logic with converse for finite ordered trees is proved.
Automated reasoning on trees with cardinality constraints
TLDR
This thesis studies efficient reasoning frameworks able to express counting constraints on tree structures using mu-calculus, and shows that the logic with counting constraints is decidable in single exponential time.
...
...

References

SHOWING 1-10 OF 62 REFERENCES
Expressive and efficient pattern languages for tree-structured data (extended abstract)
It would be desirable to have a query language for tree-structured data that is (1) as easily usable as SQL, (2) as expressive as monadic second-order logic (MSO), and (3) efficiently evaluable. The
Conditional XPath, the first order complete XPath dialect
TLDR
While Core XPath may be viewed as a simple temporal logic, conditional XPath extends this with (counterparts of) the since and until operators.
Conditional XPath
TLDR
It is shown that there exists a natural expansion of Core XPath in which every first-order definable path in XML document trees is expressible, and this expansion is called Conditional XPath.
On the power of tree-walking automata
First Order Paths in Ordered Trees
We give two sufficient conditions on XPath like languages for having first order expressivity, meaning that every first order definable set of paths in an ordered node-labeled tree is definable in
eXtensible Markup Language (XML) 1.0 (Second Edition)
The Extensible Markup Language (XML) is a subset of SGML that is completely described in this document. Its goal is to enable generic SGML to be served, received, and processed on the Web in the way
Extensible Markup Language (XML)
TLDR
XML is an extremely simple dialect of SGML which is completely described in this document, to enable generic SGML to be served, received, and processed on the Web in the way that is now possible with HTML.
Variable free reasoning on finite trees
TLDR
This paper examines three modal languages that have been proposed in the model-theoretic syntax literature for describing finite ordered trees, and finds that for two of these languages this problem is EXPTIME-complete.
XML Path Language (XPath) Version 1.0
TLDR
XPath is a language for addressing parts of an XML document, designed to be used by both XSLT and XPointer, and has been endorsed by the Director as a W3C Recommendation.
First-order logic with two variables and unary temporal logic
TLDR
It is proved that FO/sup 2/ can express precisely the same properties as linear temporal logic with only the unary temporal operators: "next", "previously", "sometime in the future", and "s sometime in the past", a logic the authors denote by unary-TL.
...
...