# Inferring Attack Relations for Gradual Semantics

arXiv: https://arxiv.org/abs/2211.16118 · HTML: https://mlsanity.com/paper/2211.16118/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [Modular Semantics and Characteristics for Bipolar Weighted Argumentation Graphs](https://mlsanity.com/paper/1807.06685/) (2018)
- [A General Account of Argumentation with Preferences](https://mlsanity.com/paper/1804.06763/) (2018)
- [A Comparative Study of Ranking-based Semantics for Abstract Argumentation](https://mlsanity.com/paper/1602.01059/) (2016)
- [Empirical Evaluation of Abstract Argumentation: Supporting the Need for Bipolar and Probabilistic Approaches](https://mlsanity.com/paper/1707.09324/) (2017)
- [Equilibrium States in Numerical Argumentation Networks](https://mlsanity.com/paper/1408.6706/) (2014)
- [Argumentative inference in uncertain and inconsistent knowledge bases](https://mlsanity.com/paper/1303.1503/) (2013)
- [Preference Elicitation in Assumption-Based Argumentation](https://mlsanity.com/paper/2005.05721/) (2020)
- [Analytical Solutions for the Inverse Problem within Gradual Semantics](https://mlsanity.com/paper/2203.01201/) (2022)
- [Characterizing Realizability in Abstract Argumentation](https://mlsanity.com/paper/1603.09545/) (2016)
- [A FPTAS for the Subset Sum Problem with Real Numbers](https://mlsanity.com/paper/2110.09901/) (2021)

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

- [Abstract Weighted Based Gradual Semantics in Argumentation Theory](https://mlsanity.com/paper/2401.11472/) (2024)
- [On the Existence of an Inverse Solution for Preference-Based Reductions in Argumentation](https://mlsanity.com/paper/2604.22958/) (2026)
- [GRASP: Deterministic argument ranking in interaction graphs](https://mlsanity.com/paper/2605.19141/) (2026)

## Abstract (arXiv)

A gradual semantics takes a weighted argumentation framework as input and outputs a final acceptability degree for each argument, with different semantics performing the computation in different manners. In this work, we consider the problem of attack inference. That is, given a gradual semantics, a set of arguments with associated initial weights, and the final desirable acceptability degrees associated with each argument, we seek to determine whether there is a set of attacks on those arguments such that we can obtain these acceptability degrees. The main contribution of our work is to demonstrate that the associated decision problem, i.e., whether a set of attacks can exist which allows the final acceptability degrees to occur for given initial weights, is NP-complete for the weighted h-categoriser and cardinality-based semantics, and is polynomial for the weighted max-based semantics, even for the complete version of the problem (where all initial weights and final acceptability degrees are known). We then briefly discuss how this decision problem can be modified to find the attacks themselves and conclude by examining the partial problem where not all initial weights or final acceptability degrees may be known.