400 research outputs found

    Forgetting in Answer Set Programming with Anonymous Cycles

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    FORGET (PTDC/CCI-INF/32219/2017). NOVA LINCS (UID/CEC/04516/2019).It is now widely accepted that the operation of forgetting in the context of Answer Set Programming [10, 18] is best characterized by the so-called strong persistence, a property that requires that all existing relations between the atoms not to be forgotten be preserved. However, it has been shown that strong persistence cannot always be satisfied. What happens if we must nevertheless forget? One possibility that has been explored before is to consider weaker versions of strong persistence, although not without a cost: some relations between the atoms not to be forgotten are broken in the process. A different alternative is to enhance the logical language so that all such relations can be maintained after the forgetting operation. In this paper, we borrow from the recently introduced notion of fork [1] – a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There – which has been shown to be sufficient to overcome the problems related to satisfying strong persistence. We map this notion into the language of logic programs, enhancing it with so-called anonymous cycles, and we introduce a concrete syntactical forgetting operator over this enhanced language that we show to always obey strong persistence.publishe

    On Syntactic Forgetting Under Uniform Equivalence

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    Forgetting in Answer Set Programming (ASP) aims at reducing the language of a logic program without affecting the consequences over the remaining language. It has recently gained interest in the context of modular ASP where it allows simplifying a program of a module, making it more declarative, by omitting auxiliary atoms or hiding certain atoms/parts of the program not to be disclosed. Unlike for arbitrary programs, it has been shown that forgetting for modular ASP can always be applied, for input, output and hidden atoms, and preserve all dependencies over the remaining language (in line with uniform equivalence). However, the definition of the result is based solely on a semantic characterization in terms of HT-models. Thus, computing an actual result is a complicated process and the result commonly bears no resemblance to the original program, i.e., we are lacking a corresponding syntactic operator. In this paper, we show that there is no forgetting operator that preserves uniform equivalence (modulo the forgotten atoms) between the given program and its forgetting result by only manipulating the rules of the original program that contain the atoms to be forgotten. We then present a forgetting operator that preserves uniform equivalence and is syntactic whenever this is suitable. We also introduce a special class of programs, where syntactic forgetting is always possible, and as a complementary result, establish it as the largest known class where forgetting while preserving all dependencies is always possible.acceptedVersionPeer reviewe

    Forgetting in Modular Answer Set Programming

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    Authors R. Goncalves, M. Knorr, and J. Leite were partially supported by FCT project FORGET (PTDC/CCI-INF/32219/2017). T. Janhunen was partially supported by the Academy of Finland project 251170. R. Goncalves was partially supported by FCT grant SFRH/BPD/100906/2014. S. Woltran was supported by the Austrian Science Fund (FWF): Y698, P25521.Modular programming facilitates the creation and reuse of large software, and has recently gathered considerable interest in the context of Answer Set Programming (ASP). In this setting, forgetting, or the elimination of middle variables no longer deemed relevant, is of importance as it allows one to, e.g., simplify a program, make it more declarative, or even hide some of its parts without affecting the consequences for those parts that are relevant. While forgetting in the context of ASP has been extensively studied, its known limitations make it unsuitable to be used in Modular ASP. In this paper, we present a novel class of forgetting operators and show that such operators can always be successfully applied in Modular ASP to forget all kinds of atoms - input, output and hidden -overcoming the impossibility results that exist for general ASP. Additionally, we investigate conditions under which this class of operators preserves the module theorem in Modular ASP, thus ensuring that answer sets of modules can still be composed, and how the module theorem can always be preserved if we further allow the reconfiguration of modules.authorsversionpublishe

    On Forgetting Relations in Relational Databases

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    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

    Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

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    Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument
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