子集空间下的邻域扩张

子集空间逻辑是刻画知识及其在证据支持度提升时发生变化的一种具有拓扑逻辑风格的简单架构的模态认知逻辑。与关系语义学不同,子集空间逻辑的语义学借助"邻域"而非"可通达关系"来表达不确定性区间。邻域的缩小体现不确定性的减少;在认知语境下,这种不确定性的减少就表现为知识的增长。子集空间逻辑主要刻画邻域的缩小。与邻域缩小相对应的邻域扩张同样具有理论研究的价值,然而却没有在子集空间逻辑中得到刻画。本文在子集空间逻辑的框架下探讨邻域的扩张。主要成果是给出带有邻域扩张算子的子集空间逻辑,为其引入关系语义学和公理系统,并证明该系统的完全性。

Neighborhood Expansion in Subset Spaces

Subset space logics, originating from Moss and Parikh, have been introduced and studied as a framework for reasoning about a notion of effort in epistemic logic. The semantics of subset space logic use“neighborhoods”, rather than“accessibility relations”as in Kripke semantics. A shrink of a neighborhood stands for a decrease of epistemic uncertainty, which shows an increase of knowledge. Existing work on subset space logics has focused on the shrinking of neighborhoods. Expansion of neighborhoods, on the other hand, has not received much attention in this field. In this paper we study the expansion of neighborhoods in the framework of subset space logics. The main results are a subset space logic with an operator for neighborhood expansion, a Kripke semantics for it, and its sound and complete axiomatization.