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AIMS Mathematics

2023, Volume 8, Issue 2: 3913-3919. doi: 10.3934/math.2023195
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Communication

A Boolean model for conflict-freeness in argumentation frameworks

  • School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China
  • Received: 31 August 2022 Revised: 14 November 2022 Accepted: 22 November 2022 Published: 29 November 2022

  • MSC : 03A05

  • The Boolean models of argumentation semantics have been established in various ways. These models commonly translate the conditions of extension-based semantics into some constraints of the models. The goal of this work is to explore a simple method to build Boolean models for argumentation. In this paper, the attack relation is treated as an operator, and its value is calculated by the values of its target and source arguments. By examining the values of the attacks, a Boolean model of conflict-free sets is introduced. This novel method simplifies the existing ways by eliminating the various constraints. The conflict-free sets can be calculated by simply checking the values of the attacks.

    Citation: Jiachao Wu. A Boolean model for conflict-freeness in argumentation frameworks[J]. AIMS Mathematics, 2023, 8(2): 3913-3919. doi: 10.3934/math.2023195

    Related Papers:

  • The Boolean models of argumentation semantics have been established in various ways. These models commonly translate the conditions of extension-based semantics into some constraints of the models. The goal of this work is to explore a simple method to build Boolean models for argumentation. In this paper, the attack relation is treated as an operator, and its value is calculated by the values of its target and source arguments. By examining the values of the attacks, a Boolean model of conflict-free sets is introduced. This novel method simplifies the existing ways by eliminating the various constraints. The conflict-free sets can be calculated by simply checking the values of the attacks.


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    [1] P. M. Dung, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and $n$-person games, Artif. Intell., 77 (1995), 321–357. https://doi.org/10.1016/0004-3702(94)00041-X doi: 10.1016/0004-3702(94)00041-X
    [2] M. Caminada, On the issue of reinstatement in argumentation, In: Logics in artificial intelligence, Berlin, Heidelberg: Springer, 2006,111–123. https://doi.org/10.1007/11853886_11
    [3] B. S. Liao, L. Jin, R. C. Koons, Dynamics of argumentation systems: a division-based method, Artif. Intell., 175 (2011), 1790–1814. https://doi.org/10.1016/j.artint.2011.03.006 doi: 10.1016/j.artint.2011.03.006
    [4] F. Pu, G. M. Luo, Z. Jiang, Encoding argumentation semantics by Boolean algebra, IEICE Trans. Inform. Syst., E100-D (2017), 838–848. https://doi.org/10.1587/transinf.2016EDP7313 doi: 10.1587/transinf.2016EDP7313
    [5] F. Cerutti, S. A. Gaggl, M. Thimm, J. P. Wallner, Foundations of implementations for formal argumentation, IfCoLog J. Log. Appl., 4 (2017), 2623–2705.
    [6] J. Ahmmad, T. Mahmood, R. Chinram, A. Iampan, Some average aggregation operators based on spherical fuzzy soft sets and their applications in multi-criteria decision making, AIMS Math., 6 (2021), 7798–7832. https://doi.org/10.3934/math.2021454 doi: 10.3934/math.2021454
    [7] A. Saha, D. Dutta, S. Kar, Some new hybrid hesitant fuzzy weighted aggregation operators based on Archimedean and Dombi operations for multi-attribute decision making, Neural Comput. Appl., 33 (2021), 8753–8776. https://doi.org/10.1007/s00521-020-05623-x doi: 10.1007/s00521-020-05623-x
    [8] S. P. Ferrando, E. Onaindia, Defeasible-argumentation-based multi-agent planning, Inform. Sci., 411 (2017), 1–22. https://doi.org/10.1016/j.ins.2017.05.014 doi: 10.1016/j.ins.2017.05.014
    [9] X. D. Li, X. Y. Yang, S. J. Song, Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica, 103 (2019), 135–140. https://doi.org/10.1016/j.automatica.2019.01.031 doi: 10.1016/j.automatica.2019.01.031
    [10] X. Xie, T. D. Wei, X. D. Li, Hybrid event-triggered approach for quasi-consensus of uncertain multi-agent systems with impulsive protocols, IEEE Trans. Circuits Syst. I. Regul. Pap., 69 (2022), 872–883. https://doi.org/10.1109/TCSI.2021.3119065 doi: 10.1109/TCSI.2021.3119065
    [11] P. Baroni, G. Boella, F. Cerutti, M. Giacomin, L. van der Torre, S. Villata, On the input/output behavior of argumentation frameworks, Artif. Intell., 217 (2014), 144–197. https://doi.org/10.1016/j.artint.2014.08.004 doi: 10.1016/j.artint.2014.08.004
    [12] X. D. Li, P. Li, Input-to-state stability of nonlinear systems: event-triggered impulsive control, IEEE Trans. Automat. Control, 67 (2022), 1460–1465. https://doi.org/10.1109/TAC.2021.3063227 doi: 10.1109/TAC.2021.3063227
    [13] X. D. Li, T. X. Zhang, J. H. Wu, Input-to-state stability of impulsive systems via event-triggered impulsive control, IEEE Trans. Cybernet., 52 (2022), 7187–7195. https://doi.org/10.1109/TCYB.2020.3044003 doi: 10.1109/TCYB.2020.3044003
    [14] X. D. Li, H. T. Zhu, S. J. Song, Input-to-state stability of nonlinear systems using observer-based event-triggered impulsive control, IEEE Trans. Syst. Man Cybernet., 51 (2021), 6892–6900. https://doi.org/10.1109/TSMC.2020.2964172 doi: 10.1109/TSMC.2020.2964172
    [15] K. Atkinson, T. Bench-Capon, Argumentation schemes in AI and law, Argum. Comput., 12 (2021), 417–434. https://doi.org/10.3233/AAC-200543 doi: 10.3233/AAC-200543
    [16] I. Benedetti, S. Bistarelli, From argumentation frameworks to voting systems and back, Fund. Inform., 150 (2017), 25–48. https://doi.org/10.3233/FI-2017-1459 doi: 10.3233/FI-2017-1459
    [17] P. Baroni, F. Toni, B. Verheij, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and $n$-person games: 25 years later, Argum. Comput., 11 (2020), 1–14. https://doi.org/10.3233/AAC-200901 doi: 10.3233/AAC-200901
    [18] K. Skiba, T. Rienstra, M. Thimm, J. Heyninck, G. Kern-Isberner, Ranking extensions in abstract argumentation, In: Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, 2021, 2047–2053. https://doi.org/10.24963/ijcai.2021/282
    [19] M. G. E. Gonzalez, M. C. D. Budán, G. I. Simari, G. R. Simari, Labeled bipolar argumentation frameworks, J. Artif. Intell. Res., 70 (2021), 1557–1636. https://doi.org/10.1613/jair.1.12394 doi: 10.1613/jair.1.12394
    [20] J. C. Wu, L. Q. Li, W. H. Sun, Gödel semantics of fuzzy argumentation frameworks with consistency degrees, AIMS Math., 5 (2020), 4045–4064. https://doi.org/10.3934/math.2020260 doi: 10.3934/math.2020260
    [21] S. Y. Zhao, J. C. Wu, An efficient algorithm of fuzzy reinstatement labelling, AIMS Math., 7 (2022), 11165–11187. https://doi.org/10.3934/math.2022625 doi: 10.3934/math.2022625
    [22] L. Amgoud, D. Doder, S. Vesic, Evaluation of argument strength in attack graphs: foundations and semantics, Artif. Intell., 302 (2022), 103607. https://doi.org/10.1016/j.artint.2021.103607 doi: 10.1016/j.artint.2021.103607
    [23] P. E. Dunne, A. Hunter, P. McBurney, S. Parsons, M. Wooldridge, Weighted argument systems: basic definitions, algorithms, and complexity results, Artif. Intell., 175 (2011), 457–486. https://doi.org/10.1016/j.artint.2010.09.005 doi: 10.1016/j.artint.2010.09.005
    [24] H. X. Liu, EBL-algebras, Soft Comput., 24 (2020), 14333–14343. https://doi.org/10.1007/s00500-020-05235-6 doi: 10.1007/s00500-020-05235-6
    [25] F. Xie, H. X. Liu, Ehoops, J. Mult. Valued Logic Soft Comput., 37 (2021), 77–106.
    [26] H. X. Liu, On topology of maximal ideals of EBL-algebras, Soft Comput., 26 (2022), 4541–4552. https://doi.org/10.1007/s00500-022-06860-z doi: 10.1007/s00500-022-06860-z
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