The Tangled Derivative Logic of the Real Line and Zero-Dimensional Space
The Tangled Derivative Logic of the Real Line and Zero-Dimensional Space
复制标题
实直线与零维空间的纠缠导数逻辑
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
I. Hodkinson
中科院分区：
文献类型：
--
作者：
R. Goldblatt;I. Hodkinson
在钻石形态被解释为导数(极限点集)算子的拓扑环境中，我们研究了一个‘纠缠导数’连接词，它将所有命题都严格稠密的最大集赋给任何有限个命题集。在我们自己和其他人早期工作的基础上，我们公理出了真正的线的结果逻辑。然后，我们证明了任何零维稠密度量空间的逻辑是Kd4的‘纠缠’扩张，从而消除了以前零维空间结果中的可分性假设。这就需要麦肯锡-塔尔斯基意义上的新的“解剖引理”。我们将分析扩展到包括普适情态，并证明了KD4的纠缠扩展对于不符合Kriske语义的拓扑模型具有很强的完备性结果。
In a topological setting in which the diamond modality is interpreted as the derivative (set of limit points) operator, we study a ‘tangled derivative’ connective that assigns to any finite set of propositions the largest set in which all those propositions are strictly dense. Building on earlier work of ourselves and others we axiomatise the resulting logic of the real line. We then show that the logic of any zero-dimensional dense-initself metric space is the ‘tangled’ extension of KD4, eliminating an assumption of separability in previous results for zero-dimensional spaces. This requires new kinds of ‘dissection lemma’ in the sense of McKinsey-Tarski. We extend the analysis to include the universal modality, and also show that the tangled extension of KD4 has a strong completeness result for topological models that fails for its Kripke semantics.
DOI：
10.1016/j.apal.2009.04.002
发表时间：
2009
期刊：
20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
影响因子：
--
作者：
A. Dawar;M. Otto
通讯作者：
M. Otto