Answering SPARQL queries modulo RDF Schema with paths

SPARQL is the standard query language for RDF graphs. In its strict instantiation, it only offers querying according to the RDF semantics and would thus ignore the semantics of data expressed with respect to (RDF) schemas or (OWL) ontologies. Several extensions to SPARQL have been proposed to query RDF data modulo RDFS, i.e., interpreting the query with RDFS semantics and/or considering external ontologies. We introduce a general framework which allows for expressing query answering modulo a particular semantics in an homogeneous way. In this paper, we discuss extensions of SPARQL that use regular expressions to navigate RDF graphs and may be used to answer queries considering RDFS semantics. We also consider their embedding as extensions of SPARQL. These SPARQL extensions are interpreted within the proposed framework and their drawbacks are presented. In particular, we show that the PSPARQL query language, a strict extension of SPARQL offering transitive closure, allows for answering SPARQL queries modulo RDFS graphs with the same complexity as SPARQL through a simple transformation of the queries. We also consider languages which, in addition to paths, provide constraints. In particular, we present and compare nSPARQL and our proposal CPSPARQL. We show that CPSPARQL is expressive enough to answer full SPARQL queries modulo RDFS. Finally, we compare the expressiveness and complexity of both nSPARQL and the corresponding fragment of CPSPARQL, that we call cpSPARQL. We show that both languages have the same complexity through cpSPARQL, being a proper extension of SPARQL graph patterns, is more expressive than nSPARQL.Comment: RR-8394; alkhateeb2003

The XFM view adaptation mechanism: An essential component for XML data warehouses

In the past few years, with many organisations providing web services for business and communication purposes, large volumes of XML transactions take place on a daily basis. In many cases, organisations maintain these transactions in their native XML format due to its flexibility for xchanging data between heterogeneous systems. This XML data provides an important resource for decision support systems. As a consequence, XML technology has slowly been included within decision support systems of data warehouse systems. The problem encountered is that existing native XML database systems suffer from poor performance in terms of managing data volume and response time for complex analytical queries. Although materialised XML views can be used to improve the performance for XML data warehouses, update problems then become the bottleneck of using materialised views. Specifically, synchronising materialised views in the face of changing view definitions, remains a significant issue. In this dissertation, we provide a method for XML-based data warehouses to manage updates caused by the change of view definitions (view redefinitions), which is referred to as the view adaptation problem. In our approach, views are defined using XPath and then modelled using a set of novel algebraic operators and fragments. XPath views are integrated into a single view graph called the XML Fragment Materialisation (XFM) View Graph, where common parts between different views are shared and appear only once in the graph. Fragments within the view graph can be selected for materialisation to facilitate the view adaptation process. While changes are applied, our view adaptation algorithms can quickly determine what part of the XFM view graph is affected. The adaptation algorithms then perform a structural adaptation to update the view graph, followed by data adaptation to update materialised fragments

A collective, probabilistic approach to schema mapping using diverse noisy evidence

We propose a probabilistic approach to the problem of schema mapping. Our approach is declarative, scalable, and extensible. It builds upon recent results in both schema mapping and probabilistic reasoning and contributes novel techniques in both fields. We introduce the problem of schema mapping selection, that is, choosing the best mapping from a space of potential mappings, given both metadata constraints and a data example. As selection has to reason holistically about the inputs and the dependencies between the chosen mappings, we define a new schema mapping optimization problem which captures interactions between mappings as well as inconsistencies and incompleteness in the input. We then introduce Collective Mapping Discovery (CMD), our solution to this problem using state-of-the-art probabilistic reasoning techniques. Our evaluation on a wide range of integration scenarios, including several real-world domains, demonstrates that CMD effectively combines data and metadata information to infer highly accurate mappings even with significant levels of noise

Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs and transformations on one hand, formulas and proof terms on the other. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs and transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties

Heterogeneous verification of model transformations

Esta tesis trata sobre la verificación formal en el contexto de la Ingeniería Dirigida por Modelos (MDE por sus siglas en inglés). El paradigma propone un ciclo de vida de la ingeniería de software basado en una abstracción de su complejidad a través de la definición de modelos y en un proceso de construcción (semi)automático guiado por transformaciones de estos modelos. Nuestro propósito es abordar la verificación de transformaciones de modelos la cual incluye, por extensión, la verificación de sus modelos. Comenzamos analizando la literatura relacionada con la verificación de transformaciones de modelos para concluir que la heterogeneidad de las propiedades que interesa verificar y de los enfoques para hacerlo, sugiere la necesidad de utilizar diversos dominios lógicos, lo cual es la base de nuestra propuesta. En algunos casos puede ser necesario realizar una verificación heterogénea, es decir, utilizar diferentes formalismos para la verificación de cada una de las partes del problema completo. Además, es beneficioso permitir a los expertos formales elegir el dominio en el que se encuentran más capacitados para llevar a cabo una prueba formal. El principal problema reside en que el mantenimiento de múltiples representaciones formales de los elementos de MDE en diferentes dominios lógicos, puede ser costoso si no existe soporte automático o una relación formal clara entre estas representaciones. Motivados por esto, definimos un entorno unificado que permite la verificación formal transformaciones de modelos mediante el uso de métodos de verificación heterogéneos, de forma tal que es posible automatizar la traducción formal de los elementos de MDE entre dominios logicos. Nos basamos formalmente en la Teoría de Instituciones, la cual proporciona una base sólida para la representación de los elementos de MDE (a través de instituciones) sin depender de ningúningún dominio lógico específico. También proporciona una forma de especificar traducciones (a través de comorfismos) que preservan la semántica entre estos elementos y otros dominios lógicos. Nos basamos en estándares para la especificación de los elementos de MDE. De hecho, definimos una institución para la buena formación de los modelos especificada con una versión simplificada del MetaObject Facility y otra institución para transformaciones utilizando Query/View/Transformation Relations. No obstante, la idea puede ser generalizada a otros enfoques de transformación y lenguajes.Por último, demostramos la viabilidad del entorno mediante el desarrollo de un prototipo funcional soportado por el Heterogeneous Tool Set (HETS). HETS permite realizar una especificación heterogénea y provee facilidades para el monitoreo de su corrección global. Los elementos de MDE se conectan con otras lógicas ya soportadas en HETS (por ejemplo: lógica de primer orden, lógica modal, entre otras) a través del Common Algebraic Specification Language (CASL). Esta conexión se expresa teóricamente mediante comorfismos desde las instituciones de MDE a la institución subyacente en CASL. Finalmente, discutimos las principales contribuciones de la tesis. Esto deriva en futuras líneas de investigación que contribuyen a la adopción de métodos formales para la verificación en el contexto de MDE.This thesis is about formal verification in the context of the Model-Driven Engineering (MDE) paradigm. The paradigm proposes a software engineering life-cycle based on an abstraction from its complexity by defining models, and on a (semi)automatic construction process driven by model transformations. Our purpose is to address the verification of model transformations which includes, by extension, the verification of their models. We first review the literature on the verification of model transformations to conclude that the heterogeneity we find in the properties of interest to verify, and in the verification approaches, suggests the need of using different logical domains, which is the base of our proposal. In some cases it can be necessary to perform a heterogeneous verification, i.e. using different formalisms for the verification of each part of the whole problem. Moreover, it is useful to allow formal experts to choose the domain in which they are more skilled to address a formal proof. The main problem is that the maintenance of multiple formal representations of the MDE elements in different logical domains, can be expensive if there is no automated assistance or a clear formal relation between these representations. Motivated by this, we define a unified environment that allows formal verification of model transformations using heterogeneous verification approaches, in such a way that the formal translations of the MDE elements between logical domains can be automated. We formally base the environment on the Theory of Institutions, which provides a sound basis for representing MDE elements (as so called institutions) without depending on any specific logical domain. It also provides a way for specifying semantic-preserving translations (as so called comorphisms) from these elements to other logical domains. We use standards for the specification of the MDE elements. In fact, we define an institution for the well-formedness of models specified with a simplified version of the MetaObject Facility, and another institution for Query/View/Transformation Relations transformations. However, the idea can be generalized to other transformation approaches and languages. Finally, we evidence the feasibility of the environment by the development of a functional prototype supported by the Heterogeneous Tool Set (HETS). HETS supports heterogeneous specifications and provides capabilities for monitoring their overall correctness. The MDE elements are connected to the other logics already supported in HETS (e.g. first-order logic, modal logic, among others) through the Common Algebraic Specification Language (CASL). This connection is defined by means of comorphisms from the MDE institutions to the underlying institution of CASL. We carry out a final discussion of the main contributions of this thesis. This results in future research directions which contribute with the adoption of formal tools for the verification in the context of MDE

Unification in monoidal theories is solving linear equations over semirings

Although for numerous equational theories unification algorithms have been developed there is still a lack of general methods. In this paper we apply algebraic techniques to the study of a whole class of theories, which we call monoidal. Our approach leads to general results on the structure of unification algorithms and the unification type of such theories. An equational theory is monoidal if it contains a binary operation which is associative and commutative, an identity for the binary operation, and an arbitrary number of unary symbols which are homomorphisms for the binary operation and the identity. Monoidal theories axiomatize varieties of abelian monoids. Examples are the theories of abelian monoids (AC), idempotent abelian monoids (ACI), and abelian groups. To every monoidal theory we associate a semiring. Intuitively, semirings are rings without subtraction. We show that every unification problem in a monoidal theory can be translated into a system of linear equations over the corresponding semiring. More specifically, problems without free constants are translated into homogeneous equations. For problems with free constants inhomogeneous equations have to be solved in addition. Exploiting the correspondence between unification and linear algebra we give algebraic characterizations of the unification type of a theory. In particular, we show that with respect to unification without constants monoidal theories are either unitary or nullary. Applying Hilbert\u27s Basis Theorem we prove that theories of groups with commuting homomorphisms are unitary with respect to unification with and without constants

Provenance in Collaborative Data Sharing

This dissertation focuses on recording, maintaining and exploiting provenance information in Collaborative Data Sharing Systems (CDSS). These are systems that support data sharing across loosely-coupled, heterogeneous collections of relational databases related by declarative schema mappings. A fundamental challenge in a CDSS is to support the capability of update exchange --- which publishes a participant\u27s updates and then translates others\u27 updates to the participant\u27s local schema and imports them --- while tolerating disagreement between them and recording the provenance of exchanged data, i.e., information about the sources and mappings involved in their propagation. This provenance information can be useful during update exchange, e.g., to evaluate provenance-based trust policies. It can also be exploited after update exchange, to answer a variety of user queries, about the quality, uncertainty or authority of the data, for applications such as trust assessment, ranking for keyword search over databases, or query answering in probabilistic databases. To address these challenges, in this dissertation we develop a novel model of provenance graphs that is informative enough to satisfy the needs of CDSS users and captures the semantics of query answering on various forms of annotated relations. We extend techniques from data integration, data exchange, incremental view maintenance and view update to define the formal semantics of unidirectional and bidirectional update exchange. We develop algorithms to perform update exchange incrementally while maintaining provenance information. We present strategies for implementing our techniques over an RDBMS and experimentally demonstrate their viability in the Orchestra prototype system. We define ProQL, a query language for provenance graphs that can be used by CDSS users to combine data querying with provenance testing as well as to compute annotations for their data, based on their provenance, that are useful for a variety of applications. Finally, we develop a prototype implementation ProQL over an RDBMS and indexing techniques to speed up provenance querying, evaluate experimentally the performance of provenance querying and the benefits of our indexing techniques