In a multi-agent system, one may choose to govern the behaviour of an agent by imposing norms, which act as guidelines for how agents should act either all of the time or in given situations. However, imposing multiple norms on one or more agents may result in situations where these norms conflict over how the agent should behave. In any system with normative conflicts (such as safe reinforcement models or systems which monitor safety protocols), one must decide which norms should be followed such that the most important and most relevant norms are maintained. We introduce a new method for resolving normative conflicts through argumentation and graph colouring which is compatible with a variety of normative conflict resolution policies. We prove that this method always creates an admissible set of arguments under argumentation semantics, meaning that it produces coherent outputs. We also introduce more robust variants of this method, each building upon their predecessor to create a superior output, and we include further mathematical proof of their coherence. Our most advanced variant uses the existing concept of curtailment, where one norm may supersede another without fully eliminating it. The methods we introduce are all compatible with various pre-existing policies for resolving normative conflicts. Empirical evaluations are also performed to compare our algorithms to each other and to others in existing literature.

We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for the paired data problem. Commonly, graphical models are ordered by the submodel relationship so that the search space is a lattice, called the model inclusion lattice. We introduce a novel order between models, named the twin order. We show that, embedded with this order, the model space is a lattice that, unlike the model inclusion lattice, is distributive. Furthermore, we provide the relevant rules for the computation of the neighbours of a model. The latter are more efficient than the same operations in the model inclusion lattice, and are then exploited to achieve a more efficient exploration of the search space. These results can be applied to improve the efficiency of both greedy and Bayesian model search procedures. Here we implement a stepwise backward elimination procedure and evaluate its performance by means of simulations. Finally, the procedure is applied to learn a brain network from fMRI data where the two groups correspond to the left and right hemispheres, respectively.