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Visualizing Extensions of Argumentation Frameworks as Layered Graphs

Martin Nöllenburg, Christian Pirker, Anna Rapberger, Stefan Woltran, Jules Wulms

TL;DR

This work addresses the visualization of abstract argumentation frameworks (AFs) with an attached extension by introducing a 3-layer layered graph layout that jointly visualizes the AF and the extension $E$. It combines design decisions that emphasize admissibility- and witness-related properties, plus a formal crossing-minimization framework with a red-edge constraint (REC) and an exact ILP and a fast heuristic pipeline (AFCrossMinREC/AFCrossMin). The main contributions are the layered AF drawing design, the REC-based optimization, and the comparative evaluation showing the heuristic is fast and typically within a factor of two of the optimum crossings, enabling interactive exploration and verification of semantics. The practical impact lies in enabling clearer, verifiable visual analyses of extensions and semantics for AFs in interactive tools and research workflows.

Abstract

The visualization of argumentation frameworks (AFs) is crucial for enabling a wide applicability of argumentative tools. However, their visualization is often considered only as an accompanying part of tools for computing semantics and standard graphical representations are used. We introduce a new visualization technique that draws an AF, together with an extension (as part of the input), as a 3-layer graph layout. Our technique supports the user to more easily explore the visualized AF, better understand extensions, and verify algorithms for computing semantics. To optimize the visual clarity and aesthetics of this layout, we propose to minimize edge crossings in our 3-layer drawing. We do so by an exact ILP-based approach, but also propose a fast heuristic pipeline. Via a quantitative evaluation, we show that the heuristic is feasible even for large instances, while producing at most twice as many crossings as an optimal drawing in most cases.

Visualizing Extensions of Argumentation Frameworks as Layered Graphs

TL;DR

This work addresses the visualization of abstract argumentation frameworks (AFs) with an attached extension by introducing a 3-layer layered graph layout that jointly visualizes the AF and the extension . It combines design decisions that emphasize admissibility- and witness-related properties, plus a formal crossing-minimization framework with a red-edge constraint (REC) and an exact ILP and a fast heuristic pipeline (AFCrossMinREC/AFCrossMin). The main contributions are the layered AF drawing design, the REC-based optimization, and the comparative evaluation showing the heuristic is fast and typically within a factor of two of the optimum crossings, enabling interactive exploration and verification of semantics. The practical impact lies in enabling clearer, verifiable visual analyses of extensions and semantics for AFs in interactive tools and research workflows.

Abstract

The visualization of argumentation frameworks (AFs) is crucial for enabling a wide applicability of argumentative tools. However, their visualization is often considered only as an accompanying part of tools for computing semantics and standard graphical representations are used. We introduce a new visualization technique that draws an AF, together with an extension (as part of the input), as a 3-layer graph layout. Our technique supports the user to more easily explore the visualized AF, better understand extensions, and verify algorithms for computing semantics. To optimize the visual clarity and aesthetics of this layout, we propose to minimize edge crossings in our 3-layer drawing. We do so by an exact ILP-based approach, but also propose a fast heuristic pipeline. Via a quantitative evaluation, we show that the heuristic is feasible even for large instances, while producing at most twice as many crossings as an optimal drawing in most cases.
Paper Structure (9 sections, 2 theorems, 2 equations, 4 figures, 1 table)

This paper contains 9 sections, 2 theorems, 2 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Visualization Design
  5. Properties of Optimal Layered AF Drawings
  6. Algorithms
  7. Evaluation
  8. Conclusion
  9. ILP description

Key Result

Theorem 1

Layered AF drawings of an AF $F=(A,R)$ with stable extension $E$, with $|E|=2$, obtained by solving AFCrossMinREC and by solving AFCrossMin have the same number of total edge crossings.

Figures (4)

  • Figure 1: The same AF visualized using a force-directed layout (left), and layered AF drawings; basic (middle) and optimized (right).
  • Figure 2: When $|E|=2$, solving AFCrossMin (left) and AFCrossMinREC (right) results in equal crossing counts.
  • Figure 3: When $|E|=3$, solving AFCrossMin (left) may result in fewer crossings than solving AFCrossMinREC (right).
  • Figure 4: Optimality gap vs. instance size for 546 instances. Black and orange points show the optimality gap as a ratio, while red points show the absolute number of crossings for the heuristic. For orange points, the ILP hit the 30 minute time-out limit.

Theorems & Definitions (5)

  • Definition 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof