团队语义与递归枚举
Team Semantics and Recursive Enumerability
摘要：
众所周知，依赖逻辑捕获复杂性类NP，最近已经表明，包含逻辑捕获有序模型上的P。这些结果表明，团队语义描述复杂性理论提供了有趣的新的可能性。为了正确理解团队语义和描述复杂性之间的联系，我们引入了依赖逻辑的扩展D*，它可以精确定义有限模型的所有递归可重复类。因此，D* 提供了一种替代图灵机的计算方法。D* 的基本新功能是一个运营商，可以扩展域所考虑的模型由有限数量的新鲜元素。由于广义量词与神谕之间的密切关系，我们也研究了广义量词在团队语义中的应用。我们证明了通过引入相应的广义依赖原子，可以从一阶逻辑的量词扩张中规范地消除（1）型单调量词。
英文摘要：
It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities for descriptive complexity theory. In order to properly understand the connection between team semantics and descriptive complexity, we introduce an extension D* of dependence logic that can define exactly all recursively enumerable classes of finite models. Thus D* provides an approach to computation alternative to Turing machines. The essential novel feature in D* is an operator that can extend the domain of the considered model by a finite number of fresh elements. Due to the close relationship between generalized quantifiers and oracles, we also investigate generalized quantifiers in team semantics. We show that monotone quantifiers of type (1) can be canonically eliminated from quantifier extensions of first-order logic by introducing corresponding generalized dependence atoms.
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