Tangled modal logic for topological dynamics
Tangled modal logic for topological dynamics
复制标题
拓扑动力学的纠缠模态逻辑
DOI：
10.1016/j.apal.2011.12.018
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
D. Fernández
中科院分区：
文献类型：
--
作者：
D. Fernández
系统S4C结合了拓扑和时间形态来对动力系统进行推理。在这里，我们考虑通过将拓扑运算符的使用推广到它的多进“纠缠”解释来丰富它的语言，最初是由Dawar和Otto在不同的上下文中引入的。我们给出了扩展系统的公理化，并证明了它是健全的和完备的。它使用了连续性公理的一个版本，我们称之为纠缠连续性，并涉及到拓扑情态的多维使用。我们还证明了所得到的系统S4C∗比S4C更有表现力；具体地说，它在区分连续动力系统和不连续动力系统方面做得更好。作为推论，我们得到纠缠连续性公理不能从包括标准连续性公理在内的其他公理中得到。
The system S4C combines topological and temporal modalities to reason about dynamical systems. Here we consider enriching its language by generalizing the use of the topological operator to its polyadic ‘tangled’ interpretation, originally introduced by Dawar and Otto in a different context. We provide an axiomatization for the extended system and show that it is sound and complete. It uses a version of the continuity axiom which we call tangled continuity and involves the polyadic use of the topological modality. We also show that the resulting system, S4C∗, is more expressive than S4C; specifically, it is better at distinguishing continuous dynamical systems from discontinuous ones. As a corollary we obtain that the tangled continuity axiom cannot be derived from the other axioms, including the standard continuity axiom.
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：
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作者：
A. Dawar;M. Otto
通讯作者：
M. Otto