A framework for explaining query answers in dl-lite

An Ontology-based Data Access system is constituted by an ontology, namely a description of the concepts and the relations in a domain of interest, a database storing facts about the domain, and a mapping between the data and the ontology. In this paper, we consider ontologies expressed in the popular DL-Lite family of Description Logic, and we address the problem of computing explanations for answers to queries in an OBDA system, where queries are either positive, in particular conjunctive queries, or negative, i.e., negation of conjunctive queries. We provide the following contributions: (i) we propose a formal, comprehensive framework of explaining query answers in OBDA systems based on DL-Lite; (ii) we present an algorithm that, given a tuple returned as an answer to a positive query, and given a weighting function, examines all the explanations of the answer, and chooses the best explanation according to such function; (iii) we do the same for the answers to negative queries. Notably, on the way to get the latter result, we present what appears to be the first algorithm that computes the answers to negative queries in DL-Lite

An introduction to description logics and query rewriting

This chapter gives an overview of the description logics underlying the OWL 2 Web Ontology Language and its three tractable profiles, OWL 2 RL, OWL 2 EL and OWL 2 QL. We consider the syntax and semantics of these description logics as well as main reasoning tasks and their computational complexity. We also discuss the semantical foundations for fist-order and datalog rewritings of conjunctive queries over knowledge bases given in the OWL2 profiles, and outline the architecture of the ontology-based data access system Ontop

Inconsistency-tolerant Query Answering in Ontology-based Data Access

Ontology-based data access (OBDA) is receiving great attention as a new paradigm for managing information systems through semantic technologies. According to this paradigm, a Description Logic ontology provides an abstract and formal representation of the domain of interest to the information system, and is used as a sophisticated schema for accessing the data and formulating queries over them. In this paper, we address the problem of dealing with inconsistencies in OBDA. Our general goal is both to study DL semantical frameworks that are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We first adapt the notion of database repair to our context, and show that, according to such a notion, inconsistency-tolerant query answering is intractable, even for very simple DLs. Therefore, we propose a different repair-based semantics, with the goal of reaching a good compromise between the expressive power of the semantics and the computational complexity of inconsistency-tolerant query answering. Indeed, we show that query answering under the new semantics is first-order rewritable in OBDA, even if the ontology is expressed in one of the most expressive members of the DL-Lite family

A Multi-Layered Architecture for Collaborative and Decentralized Consequence Finding

The consequence finding problem consists in producing all the consequences of a logical theory or, depending on the application context, in a restricted subset of these consequences. When the available knowledge is naturally scattered among different sources of information, computing such consequences with respect to the global theory in a decentralized way is a challenging problem. This paper presents Somewhere2, a multilayered architecture that may be used to solve such consequence finding problems in peer-to-peer networks of collaborating entities, that may evolve over time. The general layout of this architecture is described as well as the roles of its main components. Thanks to a careful and modular design, the resulting framework is very generic. This facilitates alternative implementations of specific components as well as its extension with additional features. First experimental results are presented, illustrating the scalability and robustness of this architecture. This framework may be used as a robust building block for more advanced distributed applications, such as Peer Data Management Systems

Dealing with Inconsistencies and Updates in Description Logic Knowledge Bases

The main purpose of an "Ontology-based Information System" (OIS) is to provide an explicit description of the domain of interest, called ontology, and let all the functions of the system be based on such representation, thus freeing the users from the knowledge about the physical repositories where the real data reside. The functionalities that an OIS should provide to the user include both query answering, whose goal is to extract information from the system, and update, whose goal is to modify the information content of the system in order to reflect changes in the domain of interest. The "ontology" is a formal, high quality intentional representation of the domain, designed in such a way to avoid inconsistencies in the modeling of concepts and relationships. On the contrary, the extensional level of the system, constituted by a set of autonomous, heterogeneous data sources, is built independently from the conceptualization represented by the ontology, and therefore may contain information that is incoherent with the ontology itself. This dissertation presents a detailed study on the problem of dealing with inconsistencies in OISs, both in query answering, and in performing updates. We concentrate on the case where the knowledge base in the OISs is expressed in Description Logics, especially the logics of the DL-lite family. As for query answering, we propose both semantical frameworks that are inconsistency-tolerant, and techniques for answering unions of conjunctive queries posed to OISs under such inconsistency-tolerant semantics. As for updates, we present an approach to compute the result of updating a possibly inconsistent OIS with both insertion and deletion of extensional knowledge

Current and Future Challenges in Knowledge Representation and Reasoning

Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade

Semiring Provenance for Lightweight Description Logics

We investigate semiring provenance--a successful framework originally defined in the relational database setting--for description logics. In this context, the ontology axioms are annotated with elements of a commutative semiring and these annotations are propagated to the ontology consequences in a way that reflects how they are derived. We define a provenance semantics for a language that encompasses several lightweight description logics and show its relationships with semantics that have been defined for ontologies annotated with a specific kind of annotation (such as fuzzy degrees). We show that under some restrictions on the semiring, the semantics satisfies desirable properties (such as extending the semiring provenance defined for databases). We then focus on the well-known why-provenance, which allows to compute the semiring provenance for every additively and multiplicatively idempotent commutative semiring, and for which we study the complexity of problems related to the provenance of an axiom or a conjunctive query answer. Finally, we consider two more restricted cases which correspond to the so-called positive Boolean provenance and lineage in the database setting. For these cases, we exhibit relationships with well-known notions related to explanations in description logics and complete our complexity analysis. As a side contribution, we provide conditions on an ELHI_bot ontology that guarantee tractable reasoning.Comment: Paper currently under review. 102 page

Federated knowledge base debugging in DL-Lite A

Due to the continuously growing amount of data the federation of different and distributed data sources gained increasing attention. In order to tackle the challenge of federating heterogeneous sources a variety of approaches has been proposed. Especially in the context of the Semantic Web the application of Description Logics is one of the preferred methods to model federated knowledge based on a well-defined syntax and semantics. However, the more data are available from heterogeneous sources, the higher the risk is of inconsistency – a serious obstacle for performing reasoning tasks and query answering over a federated knowledge base. Given a single knowledge base the process of knowledge base debugging comprising the identification and resolution of conflicting statements have been widely studied while the consideration of federated settings integrating a network of loosely coupled data sources (such as LOD sources) has mostly been neglected. In this thesis we tackle the challenging problem of debugging federated knowledge bases and focus on a lightweight Description Logic language, called DL-LiteA, that is aimed at applications requiring efficient and scalable reasoning. After introducing formal foundations such as Description Logics and Semantic Web technologies we clarify the motivating context of this work and discuss the general problem of information integration based on Description Logics. The main part of this thesis is subdivided into three subjects. First, we discuss the specific characteristics of federated knowledge bases and provide an appropriate approach for detecting and explaining contradictive statements in a federated DL-LiteA knowledge base. Second, we study the representation of the identified conflicts and their relationships as a conflict graph and propose an approach for repair generation based on majority voting and statistical evidences. Third, in order to provide an alternative way for handling inconsistency in federated DL-LiteA knowledge bases we propose an automated approach for assessing adequate trust values (i.e., probabilities) at different levels of granularity by leveraging probabilistic inference over a graphical model. In the last part of this thesis, we evaluate the previously developed algorithms against a set of large distributed LOD sources. In the course of discussing the experimental results, it turns out that the proposed approaches are sufficient, efficient and scalable with respect to real-world scenarios. Moreover, due to the exploitation of the federated structure in our algorithms it further becomes apparent that the number of identified wrong statements, the quality of the generated repair as well as the fineness of the assessed trust values profit from an increasing number of integrated sources

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

On Forgetting Relations in Relational Databases

Although not usually acknowledged as such, forgetting is a crucial aspect of human reasoning. It allows us to deal with large amounts of information, pushing irrelevant details out of our consciousness so that we can focus on the essential knowledge. Motivated by its beneficial effect on the human brain, this operation has been emulated in many formalisms in the field of Knowledge Representation and Reasoning, where several approaches to forgetting have been proposed. In common, these support computer systems dealing with inaccurate or excessive information without negatively affecting the remaining knowledge. More recently, the General Data Protection Regulation’s ‘right to be forgotten’ has given additional impetus to the study of this operation. Surprisingly, forgetting has not yet been studied in relational databases, the most widespread technology for knowledge representation. This is a serious drawback that needs to be addressed, considering the prominence of databases in our society and the relevance of the operation in numerous knowledge processing tasks. In this dissertation, we take the first steps to tackle this need, proposing a theoretical investigation of forgetting relations in relational databases. We start by introducing an alternative formalisation of the relational model, which includes a novel notion of equivalence between databases. Afterwards, we look further into the problem of forgetting. We formally define the general concept of a relation forgetting operator and present concrete operators, each aligned with a distinct view on the operation and thus with its unique features. Moreover, we illustrate the operators with examples inspired by realistic situations. Finally, we evaluate them. For that, we formalise in the form of properties the requirements that guided the definition of the operators and prove that they satisfy desirable properties. Ultimately, with this work, we motivate the importance of forgetting in relational databases and lay the foundations for its study.Embora nem sempre reconhecido como tal, o esquecimento é um aspeto crucial do raciocínio humano, pois permite-nos lidar com grandes quantidades de informação, ajudandonos a concentrar no conhecimento essencial. Motivada pelo seu efeito benéfico no cérebro humano, esta operação tem sido emulada em diversos formalismos na área da Representação do Conhecimento e Raciocínio, onde várias abordagens ao esquecimento têm sido propostas. Em comum, estas apoiam sistemas informáticos a lidar com informação imprecisa ou excessiva sem afetar negativamente o restante conhecimento. Mais recentemente, o ‘direito ao esquecimento’ do Regulamento Geral sobre a Proteção de Dados deu um impulso extra ao estudo desta operação. Surpreendentemente, o esquecimento ainda não foi estudado em bases de dados relacionais, a tecnologia mais utilizada para representação de conhecimento. Este é um grave inconveniente a resolver, tendo em conta a proeminência das bases de dados na nossa sociedade e a relevância da operação em inúmeras tarefas de processamento de conhecimento. Nesta dissertação, damos os primeiros passos no sentido de fazer frente a esta necessidade, propondo uma investigação teórica do esquecimento de relações em bases de dados relacionais. Começamos por introduzir uma formalização alternativa do modelo relacional, que inclui uma nova noção de equivalência entre bases de dados. Posteriormente, analisamos mais aprofundadamente o problema do esquecimento. Definimos formalmente o conceito geral de um operador de esquecimento de relações e apresentamos operadores concretos, cada um alinhado com uma visão distinta sobre a operação e, portanto, com as suas características únicas. Ademais, ilustramos os operadores com exemplos inspirados em situações reais. Finalmente, avaliamo-los. Para isso, formalizamos sob a forma de propriedades os requisitos que orientaram a definição dos operadores e provamos que estes satisfazem propriedades desejáveis. Em última análise, com este trabalho, motivamos a importância do esquecimento em bases de dados relacionais e estabelecemos as bases para o seu estudo