Broadening Label-based Argumentation Semantics with May-Must Scales (May-Must Argumentation)

TL;DR

This paper introduces a generalized label-based argumentation semantics using May-Must scales, allowing for more nuanced acceptability judgments and addressing computational challenges with a maximally respecting labeling approach.

Contribution

It extends traditional label-based semantics with May-Must conditions, providing a more flexible framework and proposing a method to handle undecidability issues in argumentation.

Findings

Broadened semantics express mild indeterminacy in acceptability.

Maximally respecting labelings mitigate undecidability problems.

Multiple semantics and their relations are outlined.

Abstract

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.