# Modular Semantics and Characteristics for Bipolar Weighted Argumentation Graphs

arXiv: https://arxiv.org/abs/1807.06685 · HTML: https://mlsanity.com/paper/1807.06685/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2018.

## Built on by (most cited first, 23 of 23)

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- [Learning Gradual Argumentation Frameworks using Genetic Algorithms](https://mlsanity.com/paper/2106.13585/) (2021)
- [LLM-based Argument Mining meets Argumentation and Description Logics: a Unified Framework for Reasoning about Debates](https://mlsanity.com/paper/2603.02858/) (2026)
- [Double Rectified Linear Unit-based Modular Semantics for Quantitative Bipolar Argumentation Framework](https://mlsanity.com/paper/2605.02551/) (2026)
- [Argumentation for Common Ground: Finding Zones of Possible Agreement between Individuals in Conflict](https://mlsanity.com/paper/2608.15634/) (2026)
- [Contrastive Explanations in Quantitative Bipolar Argumentation Frameworks](https://mlsanity.com/paper/2609.02399/) (2026)

## Abstract (arXiv)

This paper addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. It builds on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of acceptability semantics that have been introduced in these works, and introduce the notion of a modular acceptability semantics. A semantics is modular if it cleanly separates aggregation of attacking and supporting arguments (for a given argument a) from the computation of their influence on a's initial weight. We show that the various semantics for bipolar argumentation graphs from the literature may be analysed as a composition of an aggregation function with an influence function. Based on this modular framework, we prove general convergence and divergence theorems. We demonstrate that all well-behaved modular acceptability semantics converge for all acyclic graphs and that no sum-based semantics can converge for all graphs. In particular, we show divergence of Euler-based semantics (Amgoud et al.) for certain cyclic graphs. Further, we provide the first semantics for bipolar weighted graphs that converges for all graphs.