Probabilistic abstract argumentation: an investigation with Boltzmann machines

Probabilistic argumentation and neuro-argumentative systems offer new computational perspectives for the theory and applications of argumentation, but their principled construction involve two entangled problems. On the one hand, probabilistic argumentation aims at combining the quantitative uncertainty addressed by probability theory with the qualitative uncertainty of argumentation, but probabilistic dependences amongst arguments as well as learning are usually neglected. On the other hand neuro-argumentative systems offer the opportunity to couple the computational advantages of learning and massive parallel computation from neural networks with argumentative reasoning and explanatory abilities, but the relation of probabilistic argumentation frameworks with these systems have been ignored so far. Towards the construction of neuro-argumentative systems based on probabilistic argumentation, we associate a model of abstract argumentation and the graphical model of Boltzmann machines in order to (i) account for probabilistic abstract argumentation with possible and unknown probabilistic dependences amongst arguments, (ii) learn distributions of labellings from a set of cases and (iii) sample labellings according to the learned distribution. Experiments on domain independent artificial datasets show that argumentative Boltzmann machines can be trained with conventional training procedures and compare well with conventional machines for generating labellings of arguments, with the assurance of generating grounded labellings on demand.