From fine-grained properties to broad principles for gradual argumentation: A principled spectrum

Abstract

The study of properties of gradual evaluation methods in argumentation has received increasing attention in recent years, with studies devoted to various classes of frameworks/methods leading to conceptually similar but formally distinct properties in different contexts. In this paper we provide a novel systematic analysis for this research landscape by making three main contributions. First, we identify groups of conceptually related properties in the literature, which can be regarded as based on common patterns and, using these patterns, we evidence that many further novel properties can be considered. Then, we provide a simplifying and unifying perspective for these groups of properties by showing that they are all implied by novel parametric principles of (either strict or non-strict) balance and monotonicity. Finally, we show that (instances of) these principles (and thus the group, literature and novel properties that they imply) are satisfied by several quantitative argumentation formalisms in the literature, thus confirming the principles' general validity and utility to support a compact, yet comprehensive, analysis of properties of gradual argumentation.

A parametrized ranking-based semantics compatible with persuasion principles

“…This is so because the basis of comparison is not so clear in the first place, with different proposals focusing on different properties. In [4,9], many existing semantics were compared on the basis of properties for ranking-based semantics mentioned in the literature. However, even the relevance of some axioms may be very much dependent on the context.…”

“…In light of these differences, one may be worried that the diversity of rankings could be so high that the semantics becomes too sensitive to small modifications of the parameter δ. To check this, we applied our variable-depth propagation on 1000 randomly generated argumentation frameworks 4 for different values of δ ∈ {0.001, 0.2, 0.4, 0.6, 0.8, 0.9}. Then, we measure the dissimilarity degree between two rankings from two different values of δ using the Kendall's tau coefficient [21].…”

“…= 0.1 < 0.3 = P 0.5,0 4. et al / A parametrized ranking-based semantics compatible with persuasion principles…”

Interpretability of Gradual Semantics in Abstract Argumentation

“…The definition of a new gradual semantics is often coupled with an axiomatic evaluation [1,4]. Such axioms are mainly used to better understand the behaviour of gradual semantics in specific situations.…”

“…To answer these questions, we start from the family of graded semantics [6,4], and we select two semantics which present different features so that we can show the generality of our approach to characterise the notion of impact. In particular, we select the h-categorizer semantics initially proposed by Besnard and Hunter [5] and the counting semantics from Pu et al [16].…”