Resumen de Programación lógica difusa para la gestión flexible de documentos XML. (Fuzzy Logic Programming for the Flexible Management of XML Documents)

Alejandro Luna Tedesqui

• Resumen Esta tesis presenta una extensión del popular lenguaje XPath, que ofrece respuestas una lista de respuestas ordenadas a una consulta flexible aprovechando las variantes difusas de los operadores and, or y avg para las condiciones XPath, así como dos restricciones estructurales, llamadas down y deep, para el que se asocia un cierto grado de relevancia. En la práctica, este grado es muy bajo para algunas respuestas obtenidas con la consulta original, y por lo tanto, no deberian ser calculadas, con el fin de aliviar la complejidad computacional del proceso de recuperación de información. Con el fin de mejorar la escalabilidad de nuestro intérprete para hacer frente a archivos XML grandes, hacemos uso de la capacidad de la programación lógica difusa para descartar de forma anticipada los cálculos que conducen a soluciones poco significativas (es decir, con un pobre grado de relevancia según las preferencias expresadas por los usuarios cuando usan el nuevo comando FILTER). Nuestra propuesta se ha implementado en un lenguaje lógico difuso, aprovechando los altos recursos expresivos de este paradigma declarativo para la gestion de ¿umbrales dinámicos¿ de una manera natural y eficiente. Además de utilizar nuestro entorno FLOPER para desarrollar el intérprete, también proponemos su implementación con el lenguaje estándar XQuery. Básicamente, definimos una biblioteca XQuery capaz de gestionar de forma difusa expresiones XPath, de tal manera que nuestro FuzzyXPath puede ser codificado como expresiones XQuery. Las ventajas de nuestro enfoque es que cualquier interprete XQuery puede manipular una versión borrosa de XPath mediante el uso de la biblioteca que hemos implementado. Por otro lado, se presenta un método para depurar consultas XPath, describiendo cómo las expresiones XPath puede manipularse para obtener un conjunto de consultas alternativas que coincidan con un documento XML determinado. Para cada nueva consulta, damos un ¿chance degree¿ que representa una estimación de su desviación con respecto a la expresión inicial. Nuestro trabajo se centra en proi ii porcionar a los programadores un repertorio de alternativas (que contienen nuevos comandos como las etiquetas ¿JUMP/DELETE/SWAP¿) que se pueden utilizar para obtener mas respuestas. Nuestro depurador es capaz, de la misma manera que el intérprete, de gestionar grandes documentos XML haciendo uso del comando FILTER que ignora de forma anticipada cálculos que conducen a soluciones no significativas (es decir, con un ¿chance degree¿ muy rebajado, según las preferencias del usuario). El punto clave, nuevamente, es la capacidad natural para realizar ¿umbralizacion dinámica¿ que ofrece el lenguaje lógico difuso usado para implementar la herramienta, conectando asi de alguna manera con el llamado «top-k answering problem» muy conocido en la lógica difusa y el soft-computing (o computación flexible). En cuanto a nuevas aplicaciones no estandares, en el último bloque de esta tesis reforzamos las sinergias bilaterales entre FuzzyXPath y FLOPER. En particular, nos ocupamos de fórmulas proposicionales difusas que contienen varios símbolos proposicionales vinculados con conectivos definidos en un retículo de grados de verdad más complejos que Bool. En primer lugar, recordamos un método basado en SMT (Satisfiability Modulo Theories) difuso para demostrar automáticamente teoremas en relevantes logicas con infinitos valores (incluyendo a las de ¿ukasiewicz y Gödel ). A continuación, en lugar de centrarnos en cuestiones de satisfactibilidad (es decir, demostrar la existencia de al menos un modelo) como normalmente se hace en un entorno SAT/SMT, nuestro interés se traslada al problema de encontrar un conjunto de modelos (sobre un dominio finito) para una fórmula difusa dada. Reutilizaremos un método anterior basado en la programación lógica difusa donde la fórmula se concibe como un objetivo de un árbol de derivación, proporcionado por nuestra herramienta FLOPER, que contiene en sus ramas todos los modelos de la fórmula original, junto con otras interpretaciones (obtenidas tras interpretar de forma exsaustiva cada simbolo proposicional de todas las formas posibles con respecto a un conjunto de valores recogidos en un reticulo subyacente de grados-deverdad). A continuación utilizamos la capacidad de la herramienta FuzzyXPath para explorar estos árboles de derivación una vez exportados a formato XML, con el fin de detectar automáticamente si la fórmula es una tautología, satisfactible o una contradicción. Contents 1 Introduction 1 1.1 Objectives and structure of the Thesis . . . . . . . . . . . . . . . . . 1 1.2 Fuzzy logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Fuzzy sets, aggregators and fuzzy implications . . . . . . . . 5 1.2.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3 Logic programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4 Fuzzy logic programming . . . . . . . . . . . . . . . . . . . . . . . . 25 1.5 Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2 Multi-adjoint Logic Programming and the FLOPER System 35 2.1 Multi-Adjoint Logic Programming . . . . . . . . . . . . . . . . . . . 36 2.1.1 MALP Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.1.2 MALP Procedural Semantics . . . . . . . . . . . . . . . . . . 40 2.1.3 Interpretive Steps and Cost Measures . . . . . . . . . . . . . 42 2.2 The ¿Fuzzy LOgic Programming Environment for Research¿ . . . . . 46 2.2.1 Running Programs . . . . . . . . . . . . . . . . . . . . . . . . 50 2.2.2 Execution Trees . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.2.3 Managing Lattices . . . . . . . . . . . . . . . . . . . . . . . . 56 2.2.4 Linguistic modifiers and linguistic variables . . . . . . . . . . 60 2.3 Extending Lattices and Declarative Traces . . . . . . . . . . . . . . . 63 3 The FuzzyXPath interpreter 71 3.1 A Flexible XPath Language . . . . . . . . . . . . . . . . . . . . . . . 72 3.2 Examples with DEEP and DOWN . . . . . . . . . . . . . . . . . . . 74 3.3 AVG Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.4 Thresholding Example . . . . . . . . . . . . . . . . . . . . . . . . . . 81 vii viii CONTENTS 3.5 Conjunctive/Disjunctive Connective Examples . . . . . . . . . . . . 82 3.6 Dynamic Filtering for Improving Efficiency . . . . . . . . . . . . . . 83 4 Implementation Issues 91 4.1 Multi-Adjoint Logic Programming and FuzzyXPath . . . . . . . . . 92 4.1.1 Multi-Adjoint Logic Programming . . . . . . . . . . . . . . . 92 4.1.2 MALP and FuzzyXPath . . . . . . . . . . . . . . . . . . . . 94 4.2 FuzzyXPath in FLOPER . . . . . . . . . . . . . . . . . . . . . . . 100 4.3 XQuery Library FuzzyXPath . . . . . . . . . . . . . . . . . . . . . 106 4.3.1 Elements of the Library . . . . . . . . . . . . . . . . . . . . . 108 4.3.2 Implementation of the Library . . . . . . . . . . . . . . . . . 110 4.3.3 Examples of FuzzyXPath in XQuery . . . . . . . . . . . . . 111 4.3.4 Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5 The FuzzyXPath debugger 117 5.1 Debugging XPath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.2 MALP and the XPath Debugger . . . . . . . . . . . . . . . . . . . . 125 5.3 Dynamic Filters for the Thresholded Debugging of Queries . . . . . 127 6 Applications 133 6.1 Exploring Derivation Trees with FuzzyXPath . . . . . . . . . . . . 134 6.2 FuzzyXPath for the Automatic Search of Fuzzy Formulae Models . 144 6.3 Looking for Models with FuzzyXPath . . . . . . . . . . . . . . . . 146 7 Conclusions and Future Work 155 Chapter 7 Conclusions and Future Work In this thesis we have described the foundations and implementation of a flexible extension based on fuzzy logic programming of the well-known XPath language. The new FuzzyXPath dialect takes profit of the underlying source MALP language for easily modeling a wide range of flexible operators representing different versions of conjunctions, disjunctions and other highly expressive hybrid operators for retrieving data from XML documents, as well as for constraining queries with structural and thresholding conditions. We have shown with examples how FuzzyXPath is able to express queries in which user preferences are encoded as combination of the defined flexible operators, as well as how the language ranks answers according to them. We have described the implementation which has been coded as a set of MALP rules developed under the FLOPER system. We have shown how the operators defined in FuzzyXPath have a correspondence in MALP, and how MALP is used to compute ranked answers. The main element of the implementation is the adoption of truth value trees for representing truth values in each node of an XML tree, which are used to compute the retrieval status value of each answer. Moreover, FuzzyXPath has been integrated in the MALP framework by providing semantics to fuzzy logic programs that work with trees with truth values. This has required to study the semantics of trees with truth values and operations on them in the context of multi-adjoint logic programming. Additionally, we have studied an XQuery based implementation of our proposed FuzzyXPath . An XQuery library has been implemented enabling the execution of FuzzyXPath expressions in an XQuery interpreter. The implementation in XQuery 155 156 Chapter 7. Conclusions and Future Work of FuzzyXPath required to introduce fuzzy connectives in the Boolean language XQuery, as well as represent and work with trees with truth values in XQuery. We have also studied an approach for XPath debugging. The result of the debugging process of a XPath expression is a set of alternative queries, each one associated to a chance degree. We have proposed JUMP, DELETE and SWAP operators that cover the main cases of programming errors when describing a path about a XML document. Our implemented and tested approach has a fuzzy taste in the sense that XPath expressions are debugged by relaxing the shape of path queries with chance degrees. Our debugging technique gives to programmers a chance degree for each proposed alternative by annotating wrong-points on XPath expressions. With regard to performance of the proposed FuzzyXPath language, a fuzzy command for filtering the set of ranked answers in a dynamic way has been studied, in order to reduce the runtime and complexity of computations when dealing with large files. Our idea was to create filters for prematurely disregarding those superfluous computations dealing with non-significant solutions. We have shown benchmarks of performance of our system, improved by dynamic filtering. Additionally, we have shown the mutual benefits between two different fuzzy tools developed in our research group, that is, the FLOPER programming environment and the FuzzyXPath interpreter. Initially FLOPER was conceived as a tool for implementing flexible software applications -as it is the case of FuzzyXPathcoded with the fuzzy logic language MALP and offering options for compiling fuzzy rules to standard Prolog clauses, running goals and drawing execution trees. Such trees, once modeled in XML format inside the proper FLOPER tool, can be then analyzed by the FuzzyXPath interpreter in order to discover details (such as fuzzy computed answers, possible infinite branches and so on) of the computational behavior of MALP programs after being executed into FLOPER. Moreover, we have applied this last capability of FuzzyXPath focusing exclusively on derivation trees associated to fuzzy formulae. As a result, we have presented an automatic technique useful for determining important features of such formulae (tautology, contradiction, etc...) by making use of XPath queries with a fuzzy taste. As future work we plan the following research lines. Firstly, we are interested to extend our FuzzyXPath with the handling of text content in the same line as Fulltext XPath [CDH+11]. In our current proposal, a string used in a query has exactly mach to the content of a node to be included in the answer. Full text XPath makes possible to use ¿fuzzy¿ versions of string matching to which an score is associated. 157 String comparison techniques have been largely studied in many other contexts, and they can be adapted to our work. Also, we would like to extend our FuzzyXPath with other fuzzy logic mechanism (vagueness, similarity, among others). Path and content matching in our proposed FuzzyXPath are merely syntactic, however using vague concepts and enabling similarity can lead to better results. In this line, we also find that MALP and FLOPER can be used in ontologies and the Semantic Web, following [Str05b, LS08, For11], making possible a semantic based matching of paths and content. Additionally, we are interested in top-k answering. Top-k answering has been already studied for fuzzy logic programming [SM12], and can be adapted to FLOPER. Top-k answering determines the top k answers to a query without computing the -usually wider, possibly infinite- whole set of solutions, which is strongly related with the FILTER command. Finally, we are interested to incorporate more mechanisms of searching, ranking, debugging and filtering to the standard XQuery language. 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