Team Logic and Second-Order Logic
Team Logic and Second-Order Logic
复制标题
团队逻辑和二阶逻辑
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Ville Nurmi
中科院分区：
文献类型：
--
作者：
J. Kontinen;Ville Nurmi
团队逻辑是 Vaananen [1] 引入的一种新逻辑，通过经典否定扩展了依赖逻辑。依赖性逻辑向一阶逻辑添加了表达变量相互之间的函数依赖性的原子公式。众所周知，在句子层面上，依赖逻辑和团队逻辑分别等价于存在二阶逻辑和完全二阶逻辑。在本文中，我们表明，从某种意义上说，团队逻辑和二阶逻辑在开放公式方面也是等效的。类似的早期结果将依赖逻辑的开放公式与存在二阶逻辑的否定片段相关联，在[2]中得到了证明。
Team logic is a new logic, introduced by Vaananen [1], extending dependence logic by classical negation. Dependence logic adds to first-order logic atomic formulas expressing functional dependence of variables on each other. It is known that on the level of sentences dependence logic and team logic are equivalent with existential second-order logic and full second-order logic, respectively. In this article we show that, in a sense that we make explicit, team logic and second-order logic are also equivalent with respect to open formulas. A similar earlier result relating open formulas of dependence logic to the negative fragment of existential second-order logic was proved in [2].