Inferring Attack Relations for Gradual Semantics

TL;DR

This paper investigates the computational complexity of inferring attack relations in weighted argumentation frameworks, showing NP-completeness for some semantics and polynomial-time solvability for others, with implications for understanding argumentation dynamics.

Contribution

It establishes the complexity classifications of attack inference problems across different semantics in weighted argumentation frameworks.

Findings

NP-complete for weighted h-categoriser and cardinality-based semantics.

Polynomial-time solvable for weighted max-based semantics.

Discusses modifications for attack detection and partial information scenarios.

Abstract

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.