故障智能体认知逻辑的单纯模型
Simplicial Models for the Epistemic Logic of Faulty Agents
AI总结：
本文系统分类非纯单纯模型的设计选择并公理化相应认知逻辑，以支持参与智能体数量可变的场景，并通过分布式计算崩溃示例加以说明。
摘要：
近年来，多位作者一直在研究单纯模型，这是一种基于高维结构（称为单纯复形）的认知逻辑模型。在最初的表述中，单纯模型总是被假定为纯的，这意味着所有世界具有相同的维度。这等价于基于克里普克模型的认知逻辑的标准S5n语义。通过移除模型必须是纯的假设，我们可以超越通常的克里普克语义，研究参与某个世界的智能体数量可以变化的认知逻辑。这种方法已在多篇论文中得到发展，应用于容错分布式计算中，其中进程可能在系统执行期间崩溃。出现的一个困难是，在定义非纯单纯模型时，微妙的设计选择可能导致所得逻辑的不同公理。在本文中，我们系统地分类了这些设计选择，并对相应的逻辑进行了公理化。我们通过同步系统中进程可能崩溃的分布式计算示例来说明它们。
英文摘要：
In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher-dimensional structures called simplicial complexes. In the original formulation, simplicial models were always assumed to be pure, meaning that all worlds have the same dimension. This is equivalent to the standard S5n semantics of epistemic logic, based on Kripke models. By removing the assumption that models must be pure, we can go beyond the usual Kripke semantics and study epistemic logics where the number of agents participating in a world can vary. This approach has been developed in a number of papers, with applications in fault-tolerant distributed computing where processes may crash during the execution of a system. A difficulty that arises is that subtle design choices in the definition of impure simplicial models can result in different axioms of the resulting logic. In this paper, we classify those design choices systematically, and axiomatize the corresponding logics. We illustrate them via distributed computing examples of synchronous systems where processes may crash.
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