Normative systems represented as hybrid knowledge bases

Normative systems have been advocated as an effective tool to regulate interaction in multi-agent systems. Logic programming rules intuitively correspond to conditional norms, and their semantics is based on the closed world assumption, which allows default negation, often used in norms. However, there are cases where the closed world assumption is clearly not adequate, and others that require reasoning about unknown individuals, which is not possible in logic programming. On the other hand, description logics are based on the open world assumption and support reasoning about unknown individuals, but do not support default negation. In this paper, we demonstrate the need for the aforementioned features (closed and open world assumptions, and reasoning about unknown individuals) in order to model human laws, with examples from the Portuguese Penal Code. We advocate the use of hybrid knowledge bases combining rules and ontologies, which provide the joint expressivity of logic programming and description logics. We define a normative scenario as the pair of a set of facts and a set of norms, and give it a formal semantics by translation into an MKNF knowledge base. We describe the implementation of the language, which computes the relevant consequences of given facts and norms, and use it to establish the resulting sentence in a penal scenario.