Acceptability Semantics for Weighted Argumentation Frameworks

Abstract

The paper studies semantics that evaluate arguments in argumentation graphs, where each argument has a basic strength, and may be attacked by other arguments. It starts by defining a set of principles, each of which is a property that a semantics could satisfy. It provides the first formal analysis and comparison of existing semantics. Finally, it defines three novel semantics that satisfy more principles than existing ones.

Measuring the Intensity of Attacks in Argumentation Graphs with Shapley Value

“…The monotonicity property ensures that attacks cannot be beneficial for arguments. It is worth pointing out that this property is different from the monotony axiom from [Amgoud and Ben-Naim, 2016;Amgoud et al, 2017], which states the following: if the attackers of an argument a are also attackers of b, then a is at least as acceptable as b. This axiom assumes that a and b are in the same graph, thus the attackers of both arguments have fixed acceptability degrees.…”

“…It was shown in [Amgoud and Ben-Naim, 2016] that hcategorizer is in accordance with Definition 3, and is syntaxindependent. We implemented this semantics, and run several experiments, which all show that the semantics is monotone.…”

“…for any a ∈ A, if Att A (a) = ∅, then Deg Throughout the paper, the semantics is left unspecified. However, without loss of generality, it satisfies the very basic syntax-independence, proposed in [Amgoud et al, 2017], and monotonicity properties. The former ensures that the acceptability degree of an argument is independent of the argument's identity.…”

“…The idea is: If an argument is not attacked, then it keeps its full basic strength, otherwise it may lose weight if its attackers are sufficiently strong. In [Amgoud et al, 2017], we provided an axiomatic justification for this definition of semantics.…”

“…Recently, Amgoud et al [2016;2017] have argued that the acceptability degree of an argument should be equal to the basic strength of the argument, if the latter is not attacked. Otherwise, the argument is weakened by its attackers and thus looses weight, leading to an acceptability degree lower than the basic strength.…”