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.

翻译：渐进语义以加权论证框架为输入，为每个论点输出最终可接受度，不同语义以不同方式执行计算。本研究考虑攻击推断问题：即给定渐进语义、一组具有初始权重的论点以及每个论点的期望最终可接受度，我们试图确定是否存在一组针对这些论点的攻击关系，使得能够获得这些可接受度。本研究的主要贡献在于证明相关决策问题（即对于给定初始权重，是否存在一组攻击关系使得最终可接受度得以实现）对于加权h-分类器语义和基数基语义而言是NP完全的，而对于加权最大基语义（即使是问题的完整版本，即已知所有初始权重和最终可接受度）则是多项式的。随后，我们简要讨论如何修改此决策问题以找到攻击关系本身，并通过分析部分初始权重或最终可接受度未知的不完全问题作为结论。