论文标题
毫无用处：完整的动态拓扑逻辑
Untangled: A Complete Dynamic Topological Logic
论文作者
论文摘要
动态拓扑逻辑（$ \ mathbf {dtl} $）是一种三曲逻辑，旨在推理动态拓扑系统。费尔南德·德克（Fernández-Duque）表明，$ \ mathbf {dtl} $的自然公理集是不完整的，但他以扩展语言提供了完整的公理化。在本文中，我们考虑在散落空间上的动态拓扑逻辑，这是每个非空间空间都有一个孤立点的拓扑空间。散射空间出现在计算逻辑的背景下，因为它们为可预订性提供语义并享受可确定的固定点。我们在原始三座语言中展示了第一个声音和完整的动态拓扑逻辑。特别是，我们表明，基于散射空间类别的$ \ mathbf {dtl} $的版本在原始语言上是有限的公理，并且自然的公理化是合理的和完整的。
Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fernández-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a complete axiomatisation in an extended language. In this paper, we consider dynamic topological logic over scattered spaces, which are topological spaces where every nonempty subspace has an isolated point. Scattered spaces appear in the context of computational logic as they provide semantics for provability and enjoy definable fixed points. We exhibit the first sound and complete dynamic topological logic in the original trimodal language. In particular, we show that the version of $\mathbf{DTL}$ based on the class of scattered spaces is finitely axiomatisable over the original language, and that the natural axiomatisation is sound and complete.
