Disagree and Commit: Degrees of Argumentation-based Agreements

TL;DR

This work formalizes how autonomous agents can reach partial, robust agreements in dynamic settings using abstract and value-based argumentation. It defines degrees of satisfaction and multiple notions of degrees of agreement (minimal, mean, median) and extends these concepts to both abstract frameworks and value-based frameworks, including expansions via relaxed monotony principles. The paper provides theoretical bounds on how agreements change when new arguments are added, along with an implementation and empirical-like investigations using synthetic data to illustrate stability and value-impact effects. The approach offers a principled basis for the practical notion of disagreeing but committing in multi-agent decision-making, with potential applications in group decision support and autonomous collaboration.

Abstract

In cooperative human decision-making, agreements are often not total; a partial degree of agreement is sufficient to commit to a decision and move on, as long as one is somewhat confident that the involved parties are likely to stand by their commitment in the future, given no drastic unexpected changes. In this paper, we introduce the notion of agreement scenarios that allow artificial autonomous agents to reach such agreements, using formal models of argumentation, in particular abstract argumentation and value-based argumentation. We introduce the notions of degrees of satisfaction and (minimum, mean, and median) agreement, as well as a measure of the impact a value in a value-based argumentation framework has on these notions. We then analyze how degrees of agreement are affected when agreement scenarios are expanded with new information, to shed light on the reliability of partial agreements in dynamic scenarios. An implementation of the introduced concepts is provided as part of an argumentation-based reasoning software library.

Figures (7)

• Figure 1: Abstract argumentation framework (Example \ref{['example-2']}). Here and henceforth, arguments in gray are in all extensions (here, assuming stage semantics); arguments with dashed border are in no extension. Arguments in white with a solid border would be in some, but not in all extensions (cf. Figure \ref{['fig:example-2']}) or indicate that no semantics has been applied to infer extensions (cf. Figure \ref{['fig:example-exp']}).
• Figure 2: Abstract argumentation framework (Example \ref{['example-3']}).
• Figure 3: Argumentation frameworks and their expansions: $AF_1$ is an expansion, but not a normal expansion, of $AF_0$; $AF_2$ is a normal expansion of $AF_1$.
• Figure 4: Stage semantics violates cautious monotony: expanding $AF'$ with the "self-attacking" argument $\mathsf{c}$ and an attack from $\mathsf{b}$ to $\mathsf{c}$ is sufficient so that we can no longer infer any argument of our initial extension $\{\mathsf{a}\}$. An addition of a direct attack on the extension is not required.
• Figure 5: Example \ref{['ex:srm']}: violation of strong relaxed monotony, here assuming we apply complete, preferred, or stage semantics.

Theorems & Definitions (67)

• Example 1: Degrees of Agreement in Simple Choice Scenarios
• Example 2: Degrees of Agreement in Argumentation Scenarios
• Example 3: Degrees of Agreement in Value-based Argumentation Scenarios
• Definition 1: Admissible Set-based Argumentation Semantics dung1995acceptability
• Definition 2: Naive Set-based Argumentation Semantics verheij1996two
• Example 4
• Definition 3: Argumentation Framework Expansions and Normal Expansions baumann2010expanding
• Example 5
• Definition 4: Weak Cautious Monotony 10.1093/logcom/exab003
• Example 6