We consider the problem of implementing deontic modal logic. We show how (deontic) modal operators can be elegantly and directly expressed using default negation (negation-as-failure) and strong negation present in answer set programming (ASP). We propose using global constraints of ASP to represent obligations, prohibitions, and permissions in deontic modal logic. We show that our proposed representation results in the various decades-old paradoxes of deontic modal logic being simply and elegantly resolved. Our method also serves as a means for modeling conditional obligations and conditional prohibitions in knowledge representation.

翻译：我们研究了实现道义模态逻辑的问题。我们展示了如何利用回答集编程（ASP）中的默认否定（失败即否定）和强否定，优雅且直接地表达（道义）模态算子。我们提出使用ASP的全局约束来表示道义模态逻辑中的义务、禁止和许可。实验表明，我们提出的表示方法能够简洁而优雅地解决道义模态逻辑中数十年来的各种悖论。该方法还为知识表示中的条件义务和条件禁止提供了建模途径。