信念修正的单纯语义
Simplicial Semantics for Belief Revision
AI总结：
本文以《单纯复形中信念的一种语义》为基准修改信念语义，基于单纯模型节点为视角的概念提出两种信念修正形式化表述，并探讨迭代修正的概念陷阱及解决方案。
AI中文摘要：
本文将给出单纯语义下信念修正的定义。以《单纯复形中信念的一种语义》一文的工作为基准，本文修改了该文中给出的信念语义，使得原子公式可被指派给节点而非面。从概念和哲学角度看，若要将认知逻辑单纯模型的节点解释为特定主体的“视角”，该版本的语义更为适用。若节点是视角，那么世界（即单纯模型的面）本身由视角构成。这使我们可以说，两个世界若共享更多视角，则它们更相似或“更近”。有了这种近的概念，本文给出了两种不同的修正形式化表述。最后，本文探讨了迭代修正下这些定义周围的一些概念陷阱，并提出了一些潜在解决方案，这些方案涉及赋予主体对迄今为止所宣布内容的“记忆”。
英文摘要：
This paper will give a definition of belief revision within simplicial semantics. Starting from the work presented in "A Semantics for Belief in Simplicial Complexes" as a baseline, this paper modifies the semantics for belief given there to allow atomic formulae to be assigned to nodes, not facets. Conceptually and philosophically, this version of the semantics is better suited if one wishes to interpret the nodes of a simplicial model of epistemic logic as a "perspective" assigned to a particular agent. If nodes are perspectives, it then follows that worlds, or the facets of a simplicial model, are composed themselves of perspectives. This allows us to say that two worlds are more similar, or "nearer", if they share more perspectives. With this conceptual notion of nearness in hand, two different formal presentations of revision are given. We conclude by exploring some conceptual pitfalls surrounding these definitions under iterated revision, and motivate a few potential solutions that involve giving the agents a "memory" of what has been announced so far.
