Lexical measurements for information retrieval: a quantum approach

The problem of determining whether a document is about a loosely defined topic is at the core of text Information Retrieval (IR). An automatic IR system should be able to determine if a document is likely to convey information on a topic. In most cases, it has to do it solely based on measure- ments of the use of terms in the document (lexical measurements). In this work a novel scheme for measuring and representing lexical information from text documents is proposed. This scheme is inspired by the concept of ideal measurement as is described by Quantum Theory (QT). We apply it to Information Retrieval through formal analogies between text processing and physical measurements. The main contribution of this work is the development of a complete mathematical scheme to describe lexical measurements. These measurements encompass current ways of repre- senting text, but also completely new representation schemes for it. For example, this quantum-like representation includes logical features such as non-Boolean behaviour that has been suggested to be a fundamental issue when extracting information from natural language text. This scheme also provides a formal unification of logical, probabilistic and geometric approaches to the IR problem. From the concepts and structures in this scheme of lexical measurement, and using the principle of uncertain conditional, an “Aboutness Witness” is defined as a transformation that can detect docu- ments that are relevant to a query. Mathematical properties of the Aboutness Witness are described in detail and related to other concepts from Information Retrieval. A practical application of this concept is also developed for ad hoc retrieval tasks, and is evaluated with standard collections. Even though the introduction of the model instantiated here does not lead to substantial perfor- mance improvements, it is shown how it can be extended and improved, as well as how it can generate a whole range of radically new models and methodologies. This work opens a number of research possibilities both theoretical and experimental, like new representations for documents in Hilbert spaces or other forms, methodologies for term weighting to be used either within the proposed framework or independently, ways to extend existing methodologies, and a new range of operator-based methods for several tasks in IR

Context Dependence and Procedural Meaning: The Semantics of Definites

This thesis argues that there is a theoretically interesting connection between members of the intuitive category of context-dependent expressions, including "we", "tall", "local", "every man", "the woman", "it", "those donkeys" and so on. A treatment of the linguistic meaning of these expressions will be proposed based on the idea that their use raises issues for the audience about the proper understanding of the utterances in which they occur. The proposal will be developed in terms of a semantics for questions, which draws on the idea that to know the meaning of a question is to know what would count as an answer. It can be summarised along similar lines: to know the meaning of a context-dependent expression is to know what properties or relations (of the appropriate type) it could be used to express. The framework in which this idea will be developed can account for why the expressions that are given this issue-based treatment can also be given dependent, bound readings. The class of definite expressions, including descriptions and pronouns, is analysed in detail. A quantificational approach, where the determiner is existential, is assumed for all forms of definiteness. In all cases, the restrictor is interpreted by an atomic definite concept. The audience's grasp of the properties which definite concepts express is the result of inferential processes which take the linguistic meaning of a definite expression as input. These processes are constrained by pragmatic principles. The analysis of context-dependent expressions is extended to account for dependent interpretations. A treatment of donkey sentences that accounts for their variable quantificational force is shown to follow naturally from the analysis. A pragmatic account of infelicitous uses of definites is provided and shown to compare favourably with that provided by dynamic semantic theories. Also, a novel treatment of plural definites is provided which accounts for their variable quantificational force

Reasoning in combinations of theories

Verification problems are often expressed in a language which mixes several theories. A natural question to ask is whether one can use decision procedures for individual theories to construct a decision procedure for the union theory. In the cases where this is possible one has a powerful method at hand to handle complex theories effectively. The setup considered in this thesis is that of one base theory which is extended by one or more theories. The question is if and when a given ground satisfiability problem in the extended setting can be effectively reduced to an equi-satisfiable problem over the base theory. A case where this reductive approach is always possible is that of so-called local theory extensions. The theory of local extensions is developed and some applications concerning monotone functions are given. Then the theory of local theory extensions is generalized in order to deal with data structures that exhibit local behavior. It will be shown that a suitable fragment of both the theory of arrays and the theory of pointers is local in this broader sense. Finally, the case of more than one theory extension is discussed. In particular, a modularity result is given that under certain circumstances the locality of each of the extensions lifts to locality of the entire extension. The reductive approach outlined above has become particularly relevant in recent years due to the rise of powerful solvers for background theories common in verification tasks. These so-called SMT-solvers effectively handle theories such as real linear or integer arithmetic. As part of this thesis, a program called H-PILoT was implemented which carries out reductive reasoning for local theory extensions. H-PILoT found applications in mathematics, multiple-valued logics, data-structures and reasoning in complex systems.Verifikationsaufgaben kombinieren oft verschiedene Theorien. Eine naheliegende Frage ist, ob man Entscheidungsverfahren für die Einzeltheorien auf die gesamte Theorie übertragen kann. In den Fällen, wo das möglich ist, hat man eine mächtige Technik zur Hand, um mit komplexen Theorien effizient umgehen zu können. Der Ansatz, der in dieser Arbeit betrachtet wird, ist stets der einer Hintergrundtheorie, die durch eine oder mehrere Theorien erweitert wird. Die Frage ist dann, ob und wann sich eine gegebene Beweisanfrage bezüglich der Theorieerweiterung effektiv auf eine äquivalente Beweisanfrage bezüglich der Hintergrundtheorie reduzieren lässt. Ein Fall, in dem diese Reduzierung immer möglich ist, ist derjenige der lokalen Theorieerweiterungen. Die Theorie der lokalen Erweiterungen wird entwickelt, und es werden einige Anwendungen für monotone Funktionen gegeben. Danach wird die Theorie der lokalen Erweiterungen verallgemeinert, um mit Datenstrukturen umgehen zu können, die Lokalitätseigenschaften aufweisen. Es wird gezeigt, dass sowohl ein geeignetes Fragment der Theorie der Arrays wie auch der Theorie der Zeiger lokal im erweiterten Sinne sind. Schließlich wird der Fall mehrerer Theorieerweiterungen betrachtet. Insbesondere wird ein Modularitätsresultat gezeigt, das besagt, dass unter gewissen Umständen die Lokalität der einzelnen Erweiterungen hinreichend ist, um die Lokalität der gesamten Erweiterung zu gewährleisten. Die oben erwähnte Reduzierung von Beweisaufgaben ist in jüngster Zeit besonders relevant geworden, weil leistungsfähige Beweiser für gängige Hintergrundtheorien entwickelt worden sind. Diese sogenannten SMT-Beweiser behandeln Theorien wie z.B. lineare Arithmetik der ganzen oder der reellen Zahlen effektiv. Als Teil der vorgelegten Arbeit wurde ein Programm namens H-PILoT entwickelt, welches die Reduzierung von Beweisaufgaben für lokale Theorien durchführt. H-PILoT hat Anwendungen in der Mathematik, bei mehrwertigen Logiken, bei der Verifikation von Datenstrukturen und in der Verifikation komplexer Systeme gefunden

The role of logical interpretations on program development

Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant transformations in the context of software design, reuse, and adaptation. This paper proposes a new approach to refinement in which signature morphisms are replaced by logical interpretations as a means to witness refinements. The approach is first presented in the context of equational logic, and later generalised to deductive systems of arbitrary dimension. This allows, for example, refining sentential into equational specifications and the latter into modal ones.The authors express their gratitude to the anonymous referees who raised a number of pertinent questions entailing a more precise characterisation of the paper's contributions and a clarification of their scope. This work was funded by HRDF - European Regional Development Fund through the COMPETE Programme (operational programme for competitiveness) and by National Funds through the FCT (Portuguese Foundation for Science and Technology) within project FCOMP-01-0124-FEDER-028923 (Nasoni) and the project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690 (CIDMA-UA). The first author also acknowledges the financial assistance by the projects GetFun, reference FP7-PEOPLE-2012-IRSES, and NOCIONES IDE COMPLETUD, reference FFI2009-09345 (MICINN - Spain). A. Madeira was supported by the FCT within the project NORTE-01-0124-FEDER-000060