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.

One prominent way to deal with conflicting view-points among agents is to conduct an argumentative debate: by exchanging arguments, agents can seek to persuade each other. In this paper we investigate the problem, for an agent, of optimizing a sequence of moves to be put forward in a debate, against an opponent assumed to behave stochastically, and equipped with an unknown initial belief state. Despite the prohibitive number of states induced by a naive mapping to Markov models, we show that exploiting several features of such interaction settings allows for optimal resolution in practice, in particular: (1) as debates take place in a public space (or common ground), they can readily be modelled as Mixed Observability Markov Decision Processes, (2) as argumentation problems are highly structured, one can design optimization techniques to prune the initial instance. We report on the experimental evaluation of these techniques.