An encoding of argumentation problems using quadratic unconstrained binary optimization

TL;DR

This paper presents a novel encoding of argumentation problems as QUBO, enabling the use of quantum and classical annealing techniques for solving complex NP-Complete problems in argumentation.

Contribution

It introduces a new QUBO formulation for argumentation problems, facilitating the application of emerging quantum and digital annealing hardware.

Findings

QUBO encoding accurately models argumentation problems

Quantum and classical annealers effectively solve the encoded problems

The approach outperforms traditional approximate solvers in tests

Abstract

In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to Quadratic Unconstrained Binary Optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic function over binary variables (0/1), where the coefficients can be represented by a symmetric square matrix (or an equivalent upper triangular version). With the QUBO formulation, exploiting new computing architectures, such as Quantum and Digital Annealers, is possible. A more conventional approach consists of developing approximate solvers, which, in this case, are used to tackle the intrinsic complexity. We performed tests to prove the correctness and applicability of classical problems in Argumentation and enforcement of argument sets. We compared our approach to two other approximate solvers in the literature during tests. In the final experimentation, we used a Simulated Annealing algorithm on a local machine. Also, we tested a Quantum Annealer from the D-Wave Ocean SDK and the Leap Quantum Cloud Service.