Combining Constitutive and Regulative Norms in Input/Output Logic

In this paper we study three semantics to combine constitutive and regulative norms. In the first semantics, called the simple-minded semantics, the output of the constitutive norms are intermediate facts used as input for the regulative norms. The second method is called throughput, and adds the input of the constitutive norms to the intermediate facts. The third method is called reusable throughput, because it reuses the output of the regulative norms in the input of the constitutive norms. In addition, we refine these three so-called abstract semantics such that the obligations are labeled with the intermediate facts used to derive them. These explanations in the labels can be used for norm change, interpretation or defeasible argumentation. We present complete axiomatisations for the abstract and refined versions of the three semantics.