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A Short Introduction to Collective Defense in Weighted Abstract Argumentation Problems

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Decision Making under Constraints

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 276))

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Abstract

In this paper we review the basic ideas of weighted argumentation framework that we exploited in the last years. In particular we show how to deal with Argumentation Frameworks with weight on attacks. Such extension clearly add more information: from one side we can compare attacks measuring the added weight on the attack itself; from the other side we can aggregate attacks together using a semiring combination operator able to compute the quantitative strength of the synergy. The additional weight associated to attack relations foster a new definition of defense able to compare the weights associated to the attacks, assuring that the defense happen when it is stronger than the attack.

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Notes

  1. 1.

    In practice, c-semirings are commutative (\(\otimes \) is commutative) and idempotent semirings (i.e., \(\oplus \) is idempotent), where \(\oplus \) defines a complete lattice: every subset of elements have a least upper bound, or lub, and a greatest lower bound, or glb. In fact, c-semirings are semirings where \(\oplus \) is used as a preference operator, while \(\otimes \) is used to compose preference-values together.

  2. 2.

    Note that, when considering the partial order of a generic semiring, we will often use “worse” or “better” because “greater” or “lesser” would be misleading: in the weighted semiring, \(7 \le _{\mathbb S} 3\), i.e., lesser means better.

  3. 3.

    http://www.dmi.unipg.it/conarg/.

  4. 4.

    http://www.gecode.org.

  5. 5.

    Such properties are satisfied by a c-semiring.

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Further Reading

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Acknowledgements

We would like to thank Daniele Pirolandi, Fabio Rossi, Francesco Santini and Carlo Taticchi for unvaluable discussions and commnents that lead to the results summarised in this short paper. This research is partially supported by project “Argumentation 360” and “RACRA18” (Funded by Dept. of Mathematics and Computer Science, University of Perugia).

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  1. University of Perugia, Perugia, Italy

    Stefano Bistarelli

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  1. Stefano Bistarelli
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Correspondence to Stefano Bistarelli .

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  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  2. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Bistarelli, S. (2020). A Short Introduction to Collective Defense in Weighted Abstract Argumentation Problems. In: Ceberio, M., Kreinovich, V. (eds) Decision Making under Constraints. Studies in Systems, Decision and Control, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-030-40814-5_5

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