In this paper we introduce the novel Deontic Simplicial Logic (DSL), a deontic logic for group obligations based on simplicial complexes. We provide the first deontic interpretation of simplicial models in which vertices represent individual commitments and higher-dimensional simplices represent joint obligations of groups of agents. We further extend DSL to the Dynamic Deontic Simplicial Logic (DDSL), resulting in the first dynamic logic based on simplicial complexes. DDSL models agents' choices among mutually exclusive commitments and captures the effects of individual and joint actions via update operations on simplicial models. We prove soundness and completeness for both the static and dynamic deontic simplicial logics. We motivate our results with multiple examples, both in the static and dynamic settings.

翻译：本文提出了一种新颖的道义单纯复形逻辑（DSL），这是一种基于单纯复形的群体义务道义逻辑。我们首次对单纯复形模型进行了道义解释，其中顶点代表个体承诺，高维单纯形代表代理人群体的联合义务。我们进一步将DSL扩展为动态道义单纯复形逻辑（DDSL），从而产生了首个基于单纯复形的动态逻辑。DDSL对代理人在相互排斥的承诺间进行选择的过程进行建模，并通过单纯复形模型上的更新操作捕捉个体与联合行动的效果。我们证明了静态和动态道义单纯复形逻辑的可靠性与完备性。通过静态与动态场景下的多个实例，我们为所得结果提供了论证依据。