Learning and Reasoning about Norms using Neural-Symbolic Systems

In this paper we provide a neural-symbolic framework to model, reason about and learn norms in multi-agent systems. To this purpose, we define a fragment of Input/Output (I/O) logic that can be embedded into a neural network. We extend d’Avila Garcez et al. Connectionist Inductive Learning and Logic Programming System (CILP) to translate an I/O logic theory into a Neural Network (NN) that can be trained further with examples: we call this new system Normative- CILP (N-CILP). We then present a new algorithm to handle priorities between rules in order to cope with normative issues like Contrary to Duty (CTD), Priorities, Exceptions and Permissions. We illustrate the applicability of the framework on a case study based on RoboCup rules: within this working example, we compare the learning capacity of a network built with N-CILP with a non symbolic neural net- work, we explore how the initial knowledge impacts on the overall performance, and we test the NN capacity of learn- ing norms, generalizing new Contrary to Duty rules from examples.