Broadening Label-Based Argumentation Semantics with May-Must Scales

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, the labelling-based approach allows for a 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 mayand must-conditions for an argument to be accepted and 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 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.

Let’s Accept a Mission Impossible with Formal Argumentation, or Not

“…Compared to necessary and evidential support interpretations [13][14][15], our theory can deal with the desired causality relation generally, and can also cope with causality loops in computing acceptability semantics. Compared to (numerical) abstract persuasion argumentation [2,3], it handles causal dependency more concisely without needing a state transition system. Further, the causal-semantics have not been formulated in the dynamic argumentation theory, or in structured argumentation [11,12].…”

“…Further, the causal-semantics have not been formulated in the dynamic argumentation theory, or in structured argumentation [11,12]. For future work, it can be interesting to also consider the labelling-based semantics [2,6].…”

“…However, the level of abstractness of a dependency relation in ADF is not as high as bipolar argumentations' [7][8][9], since ultimately we have to know the conclusion as to which set of arguments are acceptable first in order to obtain matching local conditions. More abstract an approach, called may-must argumentation [2], that still respects locality is known, Unlike ADF, each argument in may-must argumentation only specifies the number of attacking arguments that have to be rejected (resp. accepted) in order that the attacked argument can be or must be accepted (resp.…”