Linear Rank Intersection Types

Non-idempotent intersection types provide quantitative information about typed programs, and have been used to obtain time and space complexity measures. Intersection type systems characterize termination, so restrictions need to be made in order to make typability decidable. One such restriction consists in using a notion of finite rank for the idempotent intersection types. In this work, we define a new notion of rank for the non-idempotent intersection types. We then define a novel type system and a type inference algorithm for the ?-calculus, using the new notion of rank 2. In the second part of this work, we extend the type system and the type inference algorithm to use the quantitative properties of the non-idempotent intersection types to infer quantitative information related to resource usage

Verification in the Hierarchical Development of Reactive Systems

In many approaches to the verification of reactive systems, operational semantics are used to model systems whereas specifications are expressed in temporal logics. Most approaches however fail to handle changes of the specification but assume, that the initial specification is indeed the intended one. Changing the specification thus necessitates to find an accordingly adapted system and to carry out the verification from scratch. During a systems life cycle however, changes of the requirements and resources necessitate repeated adaptations of specifications. We here propose a method that supports syntactic action refinement (in the process algebra TCSP and the Modal Mu-Calculus) and allows to automatically obtain (a priori) correct reactive systems by hierarchically adding details to the according specifications

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