Searching and retrieving in content-based repositories of formal mathematical knowledge

In this thesis, the author presents a query language for an RDF (Resource Description Framework) database and discusses its applications in the context of the HELM project (the Hypertextual Electronic Library of Mathematics). This language aims at meeting the main requirements coming from the RDF community. in particular it includes: a human readable textual syntax and a machine-processable XML (Extensible Markup Language) syntax both for queries and for query results, a rigorously exposed formal semantics, a graph-oriented RDF data access model capable of exploring an entire RDF graph (including both RDF Models and RDF Schemata), a full set of Boolean operators to compose the query constraints, fully customizable and highly structured query results having a 4-dimensional geometry, some constructions taken from ordinary programming languages that simplify the formulation of complex queries. The HELM project aims at integrating the modern tools for the automation of formal reasoning with the most recent electronic publishing technologies, in order create and maintain a hypertextual, distributed virtual library of formal mathematical knowledge. In the spirit of the Semantic Web, the documents of this library include RDF metadata describing their structure and content in a machine-understandable form. Using the author's query engine, HELM exploits this information to implement some functionalities allowing the interactive and automatic retrieval of documents on the basis of content-aware requests that take into account the mathematical nature of these documents.

A model and an algebra for semi-structured and full-text queries

The need for a convergence between semi-structured data management and Information Retrieval techniques is manifest to the scientific community. In order to fulfil this growing request, W3C has recently proposed XQuery Full Text, an IR-oriented extension of XQuery. However, the issue of query optimization requires the study of important properties like query equivalence and containment; to this aim, a formal representation of document and queries is needed. The goal of this thesis is to establish such formal background. We define a data model for XML documents and propose an algebra able to represent most of XQuery Full-Text expressions. We show how an XQuery Full-Text expression can be translated into an algebraic expression and how an algebraic expression can be optimized.

Towards Unstructured Knowledge Integration in Natural Language Processing

In the last decades, Artificial Intelligence has witnessed multiple breakthroughs in deep learning. In particular, purely data-driven approaches have opened to a wide variety of successful applications due to the large availability of data. Nonetheless, the integration of prior knowledge is still required to compensate for specific issues like lack of generalization from limited data, fairness, robustness, and biases. In this thesis, we analyze the methodology of integrating knowledge into deep learning models in the field of Natural Language Processing (NLP). We start by remarking on the importance of knowledge integration. We highlight the possible shortcomings of these approaches and investigate the implications of integrating unstructured textual knowledge. We introduce Unstructured Knowledge Integration (UKI) as the process of integrating unstructured knowledge into machine learning models. We discuss UKI in the field of NLP, where knowledge is represented in a natural language format. We identify UKI as a complex process comprised of multiple sub-processes, different knowledge types, and knowledge integration properties to guarantee. We remark on the challenges of integrating unstructured textual knowledge and bridge connections with well-known research areas in NLP. We provide a unified vision of structured knowledge extraction (KE) and UKI by identifying KE as a sub-process of UKI. We investigate some challenging scenarios where structured knowledge is not a feasible prior assumption and formulate each task from the point of view of UKI. We adopt simple yet effective neural architectures and discuss the challenges of such an approach. Finally, we identify KE as a form of symbolic representation. From this perspective, we remark on the need of defining sophisticated UKI processes to verify the validity of knowledge integration. To this end, we foresee frameworks capable of combining symbolic and sub-symbolic representations for learning as a solution.