[Paper Review] Measuring Inconsistency in Argument Graphs

Anthony Hunter|arXiv (Cornell University)|Aug 9, 2017

Multi-Agent Systems and Negotiation23 references4 citations

TL;DR

This paper proposes a general framework for measuring inconsistency in abstract and logic-based argument graphs, introducing structure-based and extension-based inconsistency measures. It demonstrates how these measures can guide inconsistency resolution by identifying optimal queries to reduce conflict, with empirical results showing up to a 75% reduction in inconsistency when targeting high-impact arguments.

ABSTRACT

There have been a number of developments in measuring inconsistency in logic-based representations of knowledge. In contrast, the development of inconsistency measures for computational models of argument has been limited. To address this shortcoming, this paper provides a general framework for measuring inconsistency in abstract argumentation, together with some proposals for specific measures, and a consideration of measuring inconsistency in logic-based instantiations of argument graphs, including a review of some existing proposals and a consideration of how existing logic-based measures of inconsistency can be applied.

Motivation & Objective

• To address the lack of systematic inconsistency measurement in computational argumentation models.
• To develop a general framework of postulates for measuring inconsistency in abstract argumentation graphs.
• To propose specific inconsistency measures based on graph structure and extensions.
• To adapt existing logic-based inconsistency measures for use in deductive argumentation frameworks.
• To demonstrate how inconsistency measures can guide resolution processes in real-world argumentation scenarios.

Proposed method

• Introduces a general framework of postulates for inconsistency measures in argument graphs, ensuring consistency with core rationality principles.
• Proposes structure-based measures that quantify inconsistency using graph features such as in-degree, cycle count, and connectivity.
• Develops extension-based measures that evaluate inconsistency based on the number of arguments in different labelling states (in, out, undec).
• Applies existing logic-based inconsistency measures (e.g., from [HK04, DRMO10]) to argument graphs instantiated with deductive reasoning.
• Uses query-driven commitment strategies to simulate inconsistency reduction, where each query resolves uncertainty and updates the graph structure.
• Employs a process where the argument to query is selected based on the expected reduction in inconsistency, using average reduction across possible outcomes.

Experimental results

Research questions

• RQ1 What postulates should define a rational inconsistency measure for abstract argumentation graphs?
• RQ2 How can inconsistency in argument graphs be quantified using structural and extensional features?
• RQ3 To what extent can existing logic-based inconsistency measures be adapted for use in deductive argumentation frameworks?
• RQ4 Can inconsistency measures guide effective resolution strategies in argumentation by selecting optimal queries?
• RQ5 How does inconsistency change when commitments are made to specific arguments in a graph?

Key findings

• The proposed inconsistency measures, such as $I_{in}$ and $I_{cc}$, effectively quantify the level of conflict in argument graphs, with $I_{in}(G')=4$ and $I_{cc}(G')=1$ in the initial graph $G'$.
• Querying argument $A_3$ leads to the maximum expected reduction in inconsistency, achieving a 75% reduction in $I_{in}$ when considering both possible outcomes (in/out).
• When $A_2$ is committed as in, the inconsistency drops from $I_{in}(G')=4$ to $I_{in}(G'')=1$, demonstrating a significant reduction in conflict.
• The inconsistency measure $I_{cc}$, which counts the number of cycles, decreases from 1 to 0 after resolving $A_2$ as in, indicating a reduction in structural conflict.
• The framework enables a systematic process for inconsistency resolution by selecting queries that maximize expected inconsistency reduction, improving decision-making in argumentation.
• The approach is applicable to real-world domains such as intelligence analysis, where reducing inconsistency supports better reasoning under uncertainty.