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  • Articles  (1,536)
  • Oxford University Press  (1,536)
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  • Articles  (1,536)
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  • Oxford University Press  (1,536)
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  • 1
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    On the semantics of abstract argumentation (2013)
    Oxford University Press
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    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
    Topics: Computer Science , Mathematics
    Published by Oxford University Press
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  • 2
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    Polynomial time certifying algorithms for the planar quantified integer programming problem (2013)
    Oxford University Press
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    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.
    Print ISSN: 0955-792X
    Electronic ISSN: 1465-363X
    Topics: Computer Science , Mathematics
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  • 3
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    Complexity for probability logic with quantifiers over propositions (2013)
    Oxford University Press
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    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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    Electronic ISSN: 1465-363X
    Topics: Computer Science , Mathematics
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  • 4
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    A tableau for general linear temporal logic (2013)
    Oxford University Press
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    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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    Electronic ISSN: 1465-363X
    Topics: Computer Science , Mathematics
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  • 5
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    Foundations of model construction in feature-based semantic science (2013)
    Oxford University Press
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    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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    Electronic ISSN: 1465-363X
    Topics: Computer Science , Mathematics
    Published by Oxford University Press
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  • 6
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    On a coalgebraic view on Logic (2013)
    Oxford University Press
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    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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    Topics: Computer Science , Mathematics
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  • 7
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    The expressive power of first-order topological languages (2013)
    Oxford University Press
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    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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    Topics: Computer Science , Mathematics
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  • 8
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    The cf2 argumentation semantics revisited (2013)
    Oxford University Press
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    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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    Topics: Computer Science , Mathematics
    Published by Oxford University Press
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  • 9
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    Reasoning about types of action and agent capabilities (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: We present a logical system for reasoning about types of actions (processes) and about agent capabilities to execute types of actions. The syntax of the system is based on that of Propositional Dynamic Logic ( PDL ), though the semantics we define is different (interpreting process terms as types, i.e. sets of binary relations). The standard PDL syntax is extended with capabilities statements, as in the KARO framework, atomic process types specified as precondition-effect pairs, written as , as well as backwards possibility operators. The resulting system is shown (by filtration) to have a decidable satisfiability problem and a sound and complete Gentzen-style proof system is presented.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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  • 10
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    Epsilon-invariant substitutions and indefinite descriptions (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: It is known that an epsilon-invariant sentence has a first-order reformulation, although it is not in an explicit form, since, the proof uses the non-constructive interpolation theorem. We make an attempt to describe the explicit meaning of sentences containing epsilon-terms, adopting the strong assumption of their first-order reformulability. We will prove that, if a monadic predicate is syntactically independent from an epsilon-term and if the sentence obtained by substituting the variable of the predicate with the epsilon-term is epsilon-invariant, then the sentence has an explicit first-order reformulation. Finally, we point out that the formula gives a contextual-quantificational meaning for the indefinite descriptions, provided that one accepts Kneebone’s read of epsilon-terms.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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