Relative attack strength and its application in argumentation frameworks

Jiachao Wu; Jiachao Wu

doi:10.3934/math.2025731

AIMS Mathematics

2025, Volume 10, Issue 7: 16355-16370. doi: 10.3934/math.2025731

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Research article

Relative attack strength and its application in argumentation frameworks

Jiachao Wu ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

Received: 28 March 2025 Revised: 30 June 2025 Accepted: 09 July 2025 Published: 21 July 2025
MSC : 03B52, 03E72

Adjusting the values of arguments is a widely applied method to establish the semantics of argumentation frameworks (AFs). In this process, the influence of a single attacker's value is mentioned or implicitly used many times. However, this effect has not been studied specifically. As a result, its role in semantic exploration cannot be brought into full play. Thus, my objective was to study this effect, so as to provide a new tool for semantics research. In this paper, the strength of this influence was called the relative attack strength (RAS). It was formally defined and computed by a three-variable function $ ras $. Then, nine basic properties of RAS were studied. As an application, I established a new semantics for fuzzy AFs based on RAS, which covered the Gödel semantics. The main contribution lies in the proposal of RAS and the discussion of its properties. This provides a new tool for the further study of argumentation semantics. The other contribution is the establishment of new semantics. On one hand, it fills a gap in theory. On the other hand, it shows the effectiveness of RAS in semantic research of AFs.
- argumentation framework,
- weighted argumentation framework,
- weighted arguments,
- fuzzy semantics
Citation: Jiachao Wu. Relative attack strength and its application in argumentation frameworks[J]. AIMS Mathematics, 2025, 10(7): 16355-16370. doi: 10.3934/math.2025731

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Abstract

Adjusting the values of arguments is a widely applied method to establish the semantics of argumentation frameworks (AFs). In this process, the influence of a single attacker's value is mentioned or implicitly used many times. However, this effect has not been studied specifically. As a result, its role in semantic exploration cannot be brought into full play. Thus, my objective was to study this effect, so as to provide a new tool for semantics research. In this paper, the strength of this influence was called the relative attack strength (RAS). It was formally defined and computed by a three-variable function $ ras $. Then, nine basic properties of RAS were studied. As an application, I established a new semantics for fuzzy AFs based on RAS, which covered the Gödel semantics. The main contribution lies in the proposal of RAS and the discussion of its properties. This provides a new tool for the further study of argumentation semantics. The other contribution is the establishment of new semantics. On one hand, it fills a gap in theory. On the other hand, it shows the effectiveness of RAS in semantic research of AFs.

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