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

摘要

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 VDS is defined as two fibrations: the logic for unconditional obligations OL is defined within a Cartesian closed category on the grounds of an intuitionistic propositional action logic PAL and an action logic AL, while a logic for conditional normative reasoning CNR. is defined as a symmetric closed monoidal category. A typed syntax and typed arrows are used to define properly DDS. We show how it can solve the paradoxes of deontic logic and we provide some examples of application to legal reasoning.