Formulating Semantics of Probabilistic Argumentation by Characterizing Subgraphs: Theory and Empirical Results

TL;DR

This paper introduces a novel method to efficiently compute probabilistic argumentation semantics by characterizing subgraphs, reducing reliance on simulation, and demonstrating improved computational performance especially for dense graphs.

Contribution

It defines properties to characterize subgraphs for probabilistic argumentation, enabling more efficient computation without extensive subgraph construction, and develops algorithms validated through empirical results.

Findings

Significantly reduces computation time for probabilistic semantics.

Efficiency increases with denser argumentation graphs and larger extensions.

Problems are fixed-parameter tractable under certain semantics.

Abstract

In existing literature, while approximate approaches based on Monte-Carlo simulation technique have been proposed to compute the semantics of probabilistic argumentation, how to improve the efficiency of computation without using simulation technique is still an open problem. In this paper, we address this problem from the following two perspectives. First, conceptually, we define specific properties to characterize the subgraphs of a PrAG with respect to a given extension, such that the probability of a set of arguments E being an extension can be defined in terms of these properties, without (or with less) construction of subgraphs. Second, computationally, we take preferred semantics as an example, and develop algorithms to evaluate the efficiency of our approach. The results show that our approach not only dramatically decreases the time for computing p(E^\sigma), but also has an attractive property, which is contrary to that of existing approaches: the denser the edges of a PrAG are or the bigger the size of a given extension E is, the more efficient our approach computes p(E^\sigma). Meanwhile, it is shown that under complete and preferred semantics, the problems of determining p(E^\sigma) are fixed-parameter tractable.