联合承诺的动态道义单纯逻辑
A Dynamic Deontic Simplicial Logic for Joint Commitments
AI总结：
提出基于单纯复形的道义逻辑DSL及其动态扩展DDSL，用于建模群体义务和联合承诺，并证明了可靠性和完全性。
摘要：
在本文中，我们引入了新颖的道义单纯逻辑（DSL），这是一种基于单纯复形的群体义务道义逻辑。我们首次给出了单纯模型的道义解释，其中顶点表示个体承诺，高维单纯形表示代理群体的联合义务。我们进一步将DSL扩展为动态道义单纯逻辑（DDSL），从而产生了第一个基于单纯复形的动态逻辑。DDSL对代理在互斥承诺之间的选择进行建模，并通过单纯模型上的更新操作捕捉个体和联合行动的效果。我们证明了静态和动态道义单纯逻辑的可靠性和完全性。我们通过多个静态和动态环境中的例子来论证我们的结果。
英文摘要：
We introduce the Deontic Simplicial Logic (DSL), a deontic logic for group obligations grounded in simplicial complexes: vertices encode individual commitments, and higher-dimensional simplices encode the joint commitments of the groups they connect. The resulting group modality behaves like a distributed-commitment operator with a genuinely normative character: it validates achievement but not the unrestricted introspection or monotonicity familiar from its epistemic counterpart, and impurity lets the model distinguish an agent's mere absence from a configuration from an explicit commitment to the contrary. We give a sound and complete axiomatization for the group modality. We then extend DSL to the Dynamic Deontic Simplicial Logic (DDSL), which introduces action modalities modeling agents' choices among mutually exclusive commitments, with effects captured by a product update construction on simplicial models; to our knowledge, this is the first dynamic deontic logic built on simplicial complexes. Soundness and completeness for DDSL are established via reduction axioms to the static case. Throughout, we illustrate both logics with worked examples of static and dynamic multi-agent commitment scenarios.
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