On the Existence of an Inverse Solution for Preference-Based Reductions in Argumentation

A team of computer scientists from the University of Aberdeen and CRIL (CNRS) have published a paper on arXiv (2604.22958) tackling a fundamental inverse problem in preference-based argumentation frameworks (PAFs). The problem: given a target argumentation graph, a desired labeling of arguments (e.g., accepted/rejected), and a semantics (like complete semantics), can we find a preference relation between arguments that would produce that exact outcome? This is the inverse of the standard forward problem where preferences are given and outcomes computed.

The researchers considered the four most widely-used preference-based reductions from PAFs to Dung's abstract argumentation frameworks (AAFs). Their key finding: for most cases, this inverse problem can be answered in polynomial time. This is significant because it transforms what could be an intractable search into an efficient algorithm. The work has practical implications for preference elicitation (automatically inferring user preferences from observed argument outcomes) and explainability (understanding why a particular argument was accepted or rejected based on latent preferences). The paper includes 14 pages and 2 figures, providing formal proofs and complexity analysis.