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  • Articles  (933)
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  • Articles  (933)
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  • Oxford University Press  (933)
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  • 1
    Publication Date: 2013-09-26
    Description: Arguments need to be judged against other arguments. The decision to accept or reject an argument is generally a global decision that involves examining the same question for other arguments that oppose or can defend the argument in question. This article presents the acceptability semantics for abstract argumentation that through a recursive definition gives a global assignment of the acceptable and non-acceptable subsets of arguments. This semantics stems from the aim to formalize directly the generally accepted intuition that: ‘An argument can be accepted if and only if all its challenging arguments can be rejected.’ The acceptability semantics tightly integrates the notion of defending against a challenging argument by counter-attacking it with the notion of self-defeating (or self-rejecting) arguments that (help to) bring about their own non-acceptability. The proposal is motivated by earlier studies of the semantics of Logic Programming (LP) in terms of argumentation, where the basic well founded and stable model semantics of LP can be uniformly captured using a recursively defined argumentation semantics for Negation as Failure and where these standard semantics of LP can be further extended through argumentation.
    Print ISSN: 0955-792X
    Electronic ISSN: 1465-363X
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  • 2
    Publication Date: 2013-09-26
    Description: This article is concerned with the design and analysis of polynomial time algorithms for determining whether a Planar Quantified Integer Program (PQIP) is feasible. A PQIP can be described briefly as an integer program involving two variables, in which each variable can be either universally or existentially quantified. There are four types of PQIPs, depending on how the variables are quantified (existentially or universally). In this article, we present two new, simple, and efficient algorithms for the case as well as a detailed account of the complexity of the other cases. Moreover, we discuss certification with respect to the provided algorithms.
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  • 3
    Publication Date: 2013-09-26
    Description: In the present article, the quantifiers over propositions are first introduced into the language for reasoning about probability, then the complexity issues for validity problems dealing with the corresponding hierarchy of probabilistic sentences are investigated. We prove, among other things, the $${\Pi }_{1}^{1}$$ -completeness for the general validity and also indicate the least level in the hierarchy for which the validity problem is undecidable.
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  • 4
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    Oxford University Press
    Publication Date: 2013-09-26
    Description: We use mosaics to provide a simple, sound, complete and terminating tableau reasoning procedure for the temporal logic of until and since over general linear time.
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  • 5
    Publication Date: 2013-09-26
    Description: The aim of what semantic science is to have scientific ontologies, data and hypotheses represented and published in machine understandable forms that enable predictions on new cases. There is much work on developing scientific ontologies and representing scientific data in terms of these ontologies. The next step is to publish hypotheses that can make (probabilistic) predictions on the published data and can be used for prediction on new cases. The published data can be used to evaluate hypotheses. To make a prediction in a particular case, hypotheses are combined to form models. This article considers feature-based semantic science where the data and new cases are described in terms of features. A prediction for a new case is made by building a model made up of hypotheses that fit together, are consistent with the ontologies used, and are adequate for the case. We give some desiderata for such models, and show how the construction of such models is a form of abduction. We provide a definition for models that satisfies these criteria and prove that it produces a coherent probability distribution over the values of interest.
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  • 6
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    Oxford University Press
    Publication Date: 2013-09-26
    Description: In this article we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as morphisms in a category.
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  • 7
    Publication Date: 2013-09-26
    Description: We consider the expressive power of the first-order structure 〈, C 〉 where is either of two of different domains of extended regions in Euclidean space, and C(x,y) is the topological relation ‘Region x is in contact with region y .’ We prove two main theorems: Let $$\mathcal{P}$$ [Q] be the domain of bounded, non-empty, rational polyhedra in two- or three-dimensional Euclidean space. A relation over $$\mathcal{P}$$ [Q] is definable in the structure 〈 $$\mathcal{P}$$ [Q], C 〉 if and only if is arithmetic and invariant under rational PL-homeomorphisms of the space to itself. We also extend this result to a number of other domains, including the domain of all polyhedra and the domain of semi-algebraic regions. Let $$\mathcal{R}$$ be the space of bounded, non-empty, closed regular regions in n -dimensional Euclidean space. Any analytical relation over lower dimensional (i.e. empty interior) compact point sets that is invariant under homeomorphism is implicitly definable in the structure 〈 $$\mathcal{R}$$ , C 〉.
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  • 8
    Publication Date: 2013-09-26
    Description: argumentation frameworks nowadays provide the most popular formalization of argumentation on a conceptual level. Numerous semantics for this paradigm have been proposed, whereby the cf2 semantics has shown to solve particular problems concerned with odd-length cycles in such frameworks. Due to the complicated definition of this semantics it has somehow been neglected in the literature. In this article, we introduce an alternative characterization of the cf2 semantics which, roughly speaking, avoids the recursive computation of subframeworks. This facilitates further investigation steps, like a complete complexity analysis. Furthermore, we show how the notion of strong equivalence can be characterized in terms of the cf2 semantics. In contrast to other semantics, it turns out that for the cf2 semantics strong equivalence coincides with syntactical equivalence. We make this particular behaviour more explicit by defining a new property for argumentation semantics, called the succinctness property. If a semantics satisfies the succinctness property, then for every framework F , all its attacks contribute to the evaluation of at least one framework F ' containing F . We finally characterize strong equivalence also for the stage and the naive semantics. Together with known results these characterizations imply that none of the prominent semantics for abstract argumentation, except the cf2 semantics, satisfies the succinctness property.
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  • 9
    Publication Date: 2013-09-26
    Description: The Argument Interchange Format (AIF) has been devised in order to support the interchange of ideas and data between different projects and applications in the area of computational argumentation. In order to support such interchange, an abstract ontology for argumentation is presented, which serves as an interlingua between various more concrete argumentation languages. In this article, we aim to give what is essentially a logical specification of the AIF ontology by mapping the ontology onto the logical ASPIC + framework for argumentation. We thus lay foundations for interrelating formal logic-based approaches to argumentation captured by the ASPIC + framework and the wider class of argumentation languages, including those that are more informal and user-orientated.
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  • 10
    Publication Date: 2012-09-25
    Description: This article proposes an abstract framework for argumentation-based negotiation in which the impact of exchanging arguments on agents' theories is formally described, the different types of solutions in negotiation are investigated, and the added value of argumentation in negotiation dialogues is analysed. We study when, how and to which extent an exchange of arguments can be beneficial in negotiation. The results show that argumentation can improve the quality of an outcome but never decrease it.
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