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  • 1
    Online Resource
    Online Resource
    Cambridge University Press (CUP) ; 2014
    In:  Theory and Practice of Logic Programming Vol. 14, No. 2 ( 2014-03), p. 141-164
    In: Theory and Practice of Logic Programming, Cambridge University Press (CUP), Vol. 14, No. 2 ( 2014-03), p. 141-164
    Abstract: Cardinality constraints or, more generally, weight constraints are well recognized as an important extension of answer-set programming. Clearly, all common algorithmic tasks related to programs with cardinality or weight constraints – like checking the consistency of a program – are intractable. Many intractable problems in the area of knowledge representation and reasoning have been shown to become linear time tractable if the treewidth of the programs or formulas under consideration is bounded by some constant. The goal of this paper is to apply the notion of treewidth to programs with cardinality or weight constraints and to identify tractable fragments. It will turn out that the straightforward application of treewidth to such class of programs does not suffice to obtain tractability. However, by imposing further restrictions, tractability can be achieved.
    Type of Medium: Online Resource
    ISSN: 1471-0684 , 1475-3081
    Language: English
    Publisher: Cambridge University Press (CUP)
    Publication Date: 2014
    detail.hit.zdb_id: 2045489-2
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  • 2
    Online Resource
    Online Resource
    Elsevier BV ; 2018
    In:  International Journal of Approximate Reasoning Vol. 93 ( 2018-02), p. 395-423
    In: International Journal of Approximate Reasoning, Elsevier BV, Vol. 93 ( 2018-02), p. 395-423
    Type of Medium: Online Resource
    ISSN: 0888-613X
    Language: English
    Publisher: Elsevier BV
    Publication Date: 2018
    detail.hit.zdb_id: 2002042-9
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  • 3
    Online Resource
    Online Resource
    Association for the Advancement of Artificial Intelligence (AAAI) ; 2022
    In:  Proceedings of the AAAI Conference on Artificial Intelligence Vol. 36, No. 5 ( 2022-06-28), p. 5608-5615
    In: Proceedings of the AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence (AAAI), Vol. 36, No. 5 ( 2022-06-28), p. 5608-5615
    Abstract: Argumentation frameworks (AFs) are a core formalism in the field of formal argumentation. As most standard computational tasks regarding AFs are hard for the first or second level of the Polynomial Hierarchy, a variety of algorithmic approaches to achieve manageable runtimes have been considered in the past. Among them, the backdoor-approach and the treewidth-approach turned out to yield fixed-parameter tractable fragments. However, many applications yield high parameter values for these methods, often rendering them infeasible in practice. We introduce the backdoor-treewidth approach for abstract argumentation, combining the best of both worlds with a guaranteed parameter value that does not exceed the minimum of the backdoor- and treewidth-parameter. In particular, we formally define backdoor-treewidth and establish fixed-parameter tractability for standard reasoning tasks of abstract argumentation. Moreover, we provide systems to find and exploit backdoors of small width, and conduct systematic experiments evaluating the new parameter.
    Type of Medium: Online Resource
    ISSN: 2374-3468 , 2159-5399
    Language: Unknown
    Publisher: Association for the Advancement of Artificial Intelligence (AAAI)
    Publication Date: 2022
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  • 4
    Online Resource
    Online Resource
    Association for Computing Machinery (ACM) ; 2016
    In:  ACM Transactions on Computational Logic Vol. 17, No. 3 ( 2016-07-22), p. 1-28
    In: ACM Transactions on Computational Logic, Association for Computing Machinery (ACM), Vol. 17, No. 3 ( 2016-07-22), p. 1-28
    Abstract: Recently, belief change within the framework of fragments of propositional logic has gained increasing attention. Previous research focused on belief contraction and belief revision on the Horn fragment. However, the problem of belief merging within fragments of propositional logic has been mostly neglected so far. We present a general approach to defining new merging operators derived from existing ones such that the result of merging remains in the fragment under consideration. Our approach is not limited to the case of Horn fragment; it is applicable to any fragment of propositional logic characterized by a closure property on the sets of models of its formulæ. We study the logical properties of the proposed operators regarding satisfaction of merging postulates, considering, in particular, distance-based merging operators for Horn and Krom fragments.
    Type of Medium: Online Resource
    ISSN: 1529-3785 , 1557-945X
    Language: English
    Publisher: Association for Computing Machinery (ACM)
    Publication Date: 2016
    detail.hit.zdb_id: 2025647-4
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  • 5
    Online Resource
    Online Resource
    Association for Computing Machinery (ACM) ; 2017
    In:  ACM Transactions on Computational Logic Vol. 18, No. 1 ( 2017-01-31), p. 1-32
    In: ACM Transactions on Computational Logic, Association for Computing Machinery (ACM), Vol. 18, No. 1 ( 2017-01-31), p. 1-32
    Abstract: Belief merging is a central operation within the field of belief change and addresses the problem of combining multiple, possibly mutually inconsistent knowledge bases into a single, consistent one. A current research trend in belief change is concerned with representation theorems tailored to fragments of logic, in particular Horn logic. Hereby, the goal is to guarantee that the result of the change operations stays within the fragment under consideration. While several such results have been obtained for Horn revision and Horn contraction, merging of Horn theories has been neglected so far. In this article, we provide a novel representation theorem for Horn merging by strengthening the standard merging postulates. Moreover, we present concrete Horn merging operators satisfying all postulates.
    Type of Medium: Online Resource
    ISSN: 1529-3785 , 1557-945X
    Language: English
    Publisher: Association for Computing Machinery (ACM)
    Publication Date: 2017
    detail.hit.zdb_id: 2025647-4
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  • 6
    Online Resource
    Online Resource
    Association for the Advancement of Artificial Intelligence (AAAI) ; 2018
    In:  Proceedings of the AAAI Conference on Artificial Intelligence Vol. 32, No. 1 ( 2018-04-25)
    In: Proceedings of the AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence (AAAI), Vol. 32, No. 1 ( 2018-04-25)
    Abstract: Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufficient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.
    Type of Medium: Online Resource
    ISSN: 2374-3468 , 2159-5399
    Language: Unknown
    Publisher: Association for the Advancement of Artificial Intelligence (AAAI)
    Publication Date: 2018
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  • 7
    Online Resource
    Online Resource
    IOS Press ; 2020
    In:  Fundamenta Informaticae Vol. 177, No. 3-4 ( 2020-12-10), p. 275-296
    In: Fundamenta Informaticae, IOS Press, Vol. 177, No. 3-4 ( 2020-12-10), p. 275-296
    Abstract: State-of-the-art answer set programming (ASP) solvers rely on a program called a grounder to convert non-ground programs containing variables into variable-free, propositional programs. The size of this grounding depends heavily on the size of the non-ground rules, and thus, reducing the size of such rules is a promising approach to improve solving performance. To this end, in this paper we announce lpopt, a tool that decomposes large logic programming rules into smaller rules that are easier to handle for current solvers. The tool is specifically tailored to handle the standard syntax of the ASP language (ASP-Core) and makes it easier for users to write efficient and intuitive ASP programs, which would otherwise often require significant handtuning by expert ASP engineers. It is based on an idea proposed by Morak and Woltran (2012) that we extend significantly in order to handle the full ASP syntax, including complex constructs like aggregates, weak constraints, and arithmetic expressions. We present the algorithm, the theoretical foundations on how to treat these constructs, as well as an experimental evaluation showing the viability of our approach.
    Type of Medium: Online Resource
    ISSN: 0169-2968 , 1875-8681
    Language: Unknown
    Publisher: IOS Press
    Publication Date: 2020
    detail.hit.zdb_id: 2043974-X
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  • 8
    Online Resource
    Online Resource
    Oxford University Press (OUP) ; 2016
    In:  Journal of Logic and Computation
    In: Journal of Logic and Computation, Oxford University Press (OUP)
    Type of Medium: Online Resource
    ISSN: 0955-792X , 1465-363X
    Language: English
    Publisher: Oxford University Press (OUP)
    Publication Date: 2016
    detail.hit.zdb_id: 1470328-2
    SSG: 17,1
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  • 9
    Online Resource
    Online Resource
    Oxford University Press (OUP) ; 2020
    In:  Journal of Logic and Computation Vol. 30, No. 4 ( 2020-06-05), p. 837-862
    In: Journal of Logic and Computation, Oxford University Press (OUP), Vol. 30, No. 4 ( 2020-06-05), p. 837-862
    Abstract: The notion of secure sets is a rather new concept in the area of graph theory. Applied to social network analysis, the goal is to identify groups of entities that can repel any attack or influence from the outside. In this article, we tackle this problem by utilizing Answer Set Programming (ASP). It is known that verifying whether a set is secure in a graph is already co-NP-hard. Therefore, the problem of enumerating all secure sets is challenging for ASP and its systems. In particular, encodings for this problem seem to require disjunction and also recursive aggregates. Here, we provide such encodings and analyse their performance using the Clingo system. Furthermore, we study several problem variants, including multiple secure or insecure sets, and weighted graphs.
    Type of Medium: Online Resource
    ISSN: 1465-363X , 0955-792X
    Language: English
    Publisher: Oxford University Press (OUP)
    Publication Date: 2020
    detail.hit.zdb_id: 1470328-2
    SSG: 17,1
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  • 10
    Online Resource
    Online Resource
    IOS Press ; 2013
    In:  Semantic Web Vol. 4, No. 4 ( 2013), p. 351-393
    In: Semantic Web, IOS Press, Vol. 4, No. 4 ( 2013), p. 351-393
    Type of Medium: Online Resource
    ISSN: 1570-0844
    Language: Unknown
    Publisher: IOS Press
    Publication Date: 2013
    detail.hit.zdb_id: 2599324-0
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