This paper is about the W3C standard node-addressing language for XML documents, called XPath. XPath is still under development. Version 2.0 appeared in 2001 while the theoretical foundations of Version 1.0 (dating from 1998) are still being widely studied. The paper aims at bringing XPath to a "stable fixed point" in its development: a version which is expressively complete, still manageable computationally, with a user-friendly syntax and a natural semantics.

Abstract. XPath 1.0 is a variable free language designed to specify paths between nodes in XML documents. Such paths can alternatively be specified in first-order logic. The logical abstraction of XPath 1.0, usually called Navigational or Core XPath, is not powerful enough to express every first-order definable path. In this paper we show that there exists a natural expansion of Core XPath in which every first-order definable path in XML document trees is expressible. This expansion is called Conditional XPath. It contains additional axis relations of the form (child::n[F])+, denoting the transitive closure of the path expressed by child::n[F]. The difference with XPath’s descendant::n[F] is that the path (child::n[F])+ is conditional on the fact that all nodes in between should be labeled by n and should make the predicate F true. This result can be viewed as the XPath analogue of the expressive completeness of the relational algebra with respect to first-order logic. 1

Graph database models can be characterized as those where data structures for the schema and instances are modeled as graphs or generalizations of them, and data manipulation is expressed by graph-oriented operations and type constructors. These models flourished in the eighties and early nineties in parallel to object oriented models and their influence gradually faded with the emergence of other database models, particularly the geographical, spatial, semistructured and XML. Recently, the need to manage information with inherent graph-like nature has brought back the relevance of the area. In fact, a whole new wave of applications for graph databases emerged with the development of huge networks (e.g. Web, geographical systems, transportation, telephones), and families of networks generated due to the automation of the process of data gathering (e.g. social and biological networks). The main objective of this survey is to present in a single place the work that has been done in the area of graph database modeling, concentrating in data structures, query languages and integrity constraints.

The Extensible Markup Language (XML) was designed to describe the content of a document and its hierarchical structure, and the XML Path language (XPath) is a language for selecting elements from XML documents. There is a close connection between the query processing problem for XPath and the model checking problem for temporal logics. Both boil down to checking which nodes of a graph satisfy a property. We investigate the potential of a technique based on Computation Tree Logic (CTL) model checking for evaluating queries expressed in (a subset of) XPath. To this aim, we isolate a simple fragment of XPath that is naturally embeddable into CTL. We report on experiments based on the model checker NuSMV, and compare our results with alternative academic XPath processors. We comment on the advantages and drawbacks of the application of our model checking-based approach to XPath processing.

We investigate the complexity of the model checking problem for hybrid logics. We provide model checkers for various hybrid fragments and we prove PSPACE-completeness for hybrid fragments including binders. We apply our findings to the problems of constraint verification for semistructured data and specification checking for mobile systems.

Variables in XPath 2.0 are fundamental for selecting n-tuples of nodes in trees. The navigational core of XPath 2.0 is known to capture first-order (FO) logic while being PSPACE complete with respect to model checking. In this paper, we distinguish a fragment of Core XPath 2.0 that we call the polynomial-time path language (PPL). We show that PPL remains FO-complete even though enjoying polynomial time query answering (and thus model checking).

The Ambient Logic is a modal logic proposed to describe the structural and computational properties of distributed and mobile computations.

Abstract. We study the complexity of satisfiability for the expressive extensionICPDL of PDL (Propositional Dynamic Logic), which admits intersection and converse as program operations. Our main result is containment in 2EXP, whichimproves the previously known non-elementary upper bound and implies 2EXP-completeness due to an existing lower bound for PDL with intersection. The proof

The Extensible Markup Language (XML) was designed to describe the content of a document and its hierarchical structure. The XML Path language (XPath) is a language for selecting elements from XML documents. We propose and implement a linear embedding of the query evaluation problem for Core XPath, the navigational fragment of XPath, into the model checking problem for Computation Tree Logic (CTL). We extend the embedding to XCPath, an extension of Core XPath that is as expressive as first-order logic on sibling-ordered trees. This allows us to evaluate XCPath queries by exploiting a model checker for CTL. We report on experiments with the state-of-the-art model checker NuSMV, and compare our results with alternative academic XPath processors. Acknowledgements This thesis is the result of work with several people which I will mention below. I was just being in the middle of the process, trying to catch and to learn as much as possible, about myself, about my interests, about my capacities. What I have learned actually is a great deal about the people that I got to know. I learned how people can be generous and patient, professional and loving. I had a school of life more then a school of logic. I consider this thesis to be the work of Massimo Franceschet, Maarten Marx and Balder ten Cate, as much as mine. More of mine was the pleasure of learning from them. Maarten Marx's help cannot be described in words. He has many qualities which I respect. I will mention only one. He was able always to come up with just the right solution for my problems. He o#ered help firmly, quickly, the right one and in the right moment. I wish I could be the same in this respect. Massimo Franceschet was very kind to me and brave, agreeing to be my adviser. He advised me wisely, caring more abou...

We consider in this paper rooted labeled directed graphs as models for semistructured data. A path inclusion constraint, in such graphs, is an expression p � q where p and q are regular expressions over the alphabet of labels. An path inclusion constraint p � q is satisfied by a rooted labeled directed graph if the set of nodes reached, from the root, by the words of the language described by p is included in the set of nodes reached, from the root, by the words of the language described by q. We answer here to the following problem: given a set C of path inclusion constraints, given a regular expression p describing an infinite regular language, we want to compute, if it exists, a regular expression f describing a finite language, such that p � f for every graph satisfying C. 1