The semantics as to which set of arguments in a given argumentation graph may be acceptable (acceptability semantics) can be characterised in a few different ways. Among them, labelling-based approach allows for concise and flexible determination of acceptability statuses of arguments through assignment of a label indicating acceptance, rejection, or undecided to each argument. In this work, we contemplate a way of broadening it by accommodating may- and must- conditions for an argument to be accepted or rejected, as determined by the number(s) of rejected and accepted attacking arguments. We show that the broadened label-based semantics can be used to express more mild indeterminacy than inconsistency for acceptability judgement when, for example, it may be the case that an argument is accepted and when it may also be the case that it is rejected. We identify that finding which conditions a labelling satisfies for every argument can be an undecidable problem, which has an unfavourable implication to existence of a semantics. We propose to address this problem by enforcing a labelling to maximally respect the conditions, while keeping the rest that would necessarily cause non-termination labelled undecided. Several semantics will be presented and the relation among them will be noted. Towards the end, we will touch upon possible research directions that can be pursued further.

中文翻译：

---

使用 May-Must Scales 扩展基于标签的论证语义（May-Must Argumentation）

关于给定论证图中的哪一组参数可以接受的语义（可接受性语义）可以用几种不同的方式来表征。其中，基于标签的方法允许通过为每个参数分配表示接受、拒绝或未决定的标签来简洁灵活地确定参数的可接受状态。在这项工作中，我们考虑了一种扩大它的方法，通过适应被接受或拒绝的论点的可能和必须条件，这取决于被拒绝和接受的攻击性论点的数量。我们表明，扩展的基于标签的语义可用于表达比可接受性判断的不一致更轻微的不确定性，例如，一个论点可能会被接受，也可能会被拒绝。我们发现找到标签满足每个参数的条件可能是一个不可判定的问题，这对语义的存在具有不利的影响。我们建议通过强制标记来最大程度地尊重条件来解决这个问题，同时保留其他可能导致非终止标记未定的问题。将介绍几种语义并注意它们之间的关系。最后，我们将探讨可以进一步探索的可能研究方向。我们建议通过强制标记来最大程度地尊重条件来解决这个问题，同时保留其他可能导致非终止标记未定的问题。将介绍几种语义并注意它们之间的关系。最后，我们将探讨可以进一步探索的可能研究方向。我们建议通过强制标记来最大程度地尊重条件来解决这个问题，同时保留其他可能导致非终止标记未定的问题。将介绍几种语义并注意它们之间的关系。最后，我们将探讨可以进一步探索的可能研究方向。