# A Methodology for Incompleteness-Tolerant and Modular Gradual Semantics for Argumentative Statement Graphs

arXiv: https://arxiv.org/abs/2410.22209 · HTML: https://mlsanity.com/paper/2410.22209/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 80 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 17 of 17)

- [Argumentative XAI: A Survey](https://mlsanity.com/paper/2105.11266/) (2021)
- [Interpreting Neural Networks as Gradual Argumentation Frameworks (Including Proof Appendix)](https://mlsanity.com/paper/2012.05738/) (2020)
- [Interactive Explanations by Conflict Resolution via Argumentative Exchanges](https://mlsanity.com/paper/2303.15022/) (2023)
- [Can Large Language Models perform Relation-based Argument Mining?](https://mlsanity.com/paper/2402.11243/) (2024)
- [Epistemic Graphs for Representing and Reasoning with Positive and Negative Influences of Arguments](https://mlsanity.com/paper/1802.07489/) (2018)
- [Automatic Debate Evaluation with Argumentation Semantics and Natural Language Argument Graph Networks](https://mlsanity.com/paper/2203.14647/) (2022)
- [Contribution Functions for Quantitative Bipolar Argumentation Graphs: A Principle-based Analysis](https://mlsanity.com/paper/2401.08879/) (2024)
- [Empirical Evaluation of Abstract Argumentation: Supporting the Need for Bipolar and Probabilistic Approaches](https://mlsanity.com/paper/1707.09324/) (2017)
- [Strategic Argumentation Dialogues for Persuasion: Framework and Experiments Based on Modelling the Beliefs and Concerns of the Persuadee](https://mlsanity.com/paper/2101.11870/) (2021)
- [Argument Attribution Explanations in Quantitative Bipolar Argumentation Frameworks (Technical Report)](https://mlsanity.com/paper/2307.13582/) (2023)
- [Equilibrium States in Numerical Argumentation Networks](https://mlsanity.com/paper/1408.6706/) (2014)
- [Forecasting Argumentation Frameworks](https://mlsanity.com/paper/2205.11590/) (2022)
- [Dialectical Reconciliation via Structured Argumentative Dialogues](https://mlsanity.com/paper/2306.14694/) (2023)
- [Ranking-based Argumentation Semantics Applied to Logical Argumentation (full version)](https://mlsanity.com/paper/2307.16780/) (2023)
- [CE-QArg: Counterfactual Explanations for Quantitative Bipolar Argumentation Frameworks (Technical Report)](https://mlsanity.com/paper/2407.08497/) (2024)
- [Intrinsic Argument Strength in Structured Argumentation: a Principled Approach](https://mlsanity.com/paper/2109.00318/) (2021)
- [An Interleaving Semantics of the Timed Concurrent Language for Argumentation to Model Debates and Dialogue Games](https://mlsanity.com/paper/2306.07675/) (2023)

## Built on by (most cited first, 3 of 3)

- [On Gradual Semantics for Assumption-Based Argumentation](https://mlsanity.com/paper/2507.10076/) (2025)
- [Discourse-Aware Policy Analysis with Argumentation: A Hybrid LLM-Symbolic Framework for Disaster Governance](https://mlsanity.com/paper/2607.13260/) (2026)
- [Have You Been Convinced? A Neuro-symbolic Argumentation Reasoning Approach to Detecting Persuasiveness in ChangeMyView Discussions](https://mlsanity.com/paper/2610.15091/) (2026)

## Abstract (arXiv)

Gradual semantics (GS) have demonstrated great potential in argumentation, in particular for deploying quantitative bipolar argumentation frameworks (QBAFs) in a number of real-world settings, from judgmental forecasting to explainable AI. In this paper, we provide a novel methodology for obtaining GS for statement graphs, a form of structured argumentation framework, where arguments and relations between them are built from logical statements. Our methodology differs from existing approaches in the literature in two main ways. First, it naturally accommodates incomplete information, so that arguments with partially specified premises can play a meaningful role in the evaluation. Second, it is modularly defined to leverage on any GS for QBAFs. We also define a set of novel properties for our GS and study their suitability alongside a set of existing properties (adapted to our setting) for two instantiations of our GS, demonstrating their advantages over existing approaches.