A Polynomial-time Fragment of Epistemic Probabilistic Argumentation (Technical Report)

TL;DR

This paper identifies a specific fragment of epistemic probabilistic argumentation where computational problems become tractable, enabling polynomial-time solutions through convex programming, thus addressing exponential complexity issues.

Contribution

The authors define a fragment of epistemic probabilistic argumentation that allows polynomial-time solutions for problems previously considered intractable, using convex programming methods.

Findings

Exponential complexity can be avoided in this fragment.

Certain intractable problems are solvable in polynomial time.

Convex programming formulations are effective for these problems.

Abstract

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding an exponential number of terms. We show that this exponential blowup can be avoided in an interesting fragment of epistemic probabilistic argumentation and that some computational problems that have been considered intractable can be solved in polynomial time. We give efficient convex programming formulations for these problems and explore how far our fragment can be extended without loosing tractability.