The categorical imperative: Category theory as a foundation for deontic logic

This article introduces a deontic logic which aims to model the Canadian legal discourse. Category theory is assumed as a foundational framework for logic. A deontic deductive system DDSDDS is defined as two fibrations: the logic for unconditional obligations OLOL is defined within a Cartesian closed category on the grounds of an intuitionistic propositional action logic PALPAL and an action logic ALAL, while a logic for conditional normative reasoning CNRCNR is defined as a symmetric closed monoidal category. A typed syntax and typed arrows are used to define properly DDSDDS. We show how it can solve the paradoxes of deontic logic and we provide some examples of application to legal reasoning.