多项式Ramsey量词的刻画
Characterizing Polynomial Ramsey Quantifiers
摘要：
Ramsey量词不仅是逻辑学和计算机科学的研究对象，而且也是自然语言的形式语义学的研究对象。将注意力限制在有限模型上会导致一个自然的问题，即所有的拉姆齐量词是多项式时间可计算的还是NP困难的，以及我们是否可以给出多项式时间可计算量词的自然特征。在本文中，我们首先表明，存在中间Ramsey量词，然后我们证明了一个二分法的结果，一个大的和自然类的Ramsey量词，基于一个合理的和广泛相信的复杂性假设。我们证明了该类中的多项式时间可计算量词恰好是常数对数有界的Ramsey量词。
英文摘要：
Ramsey quantifiers are a natural object of study not only for logic and computer science, but also for the formal semantics of natural language. Restricting attention to finite models leads to the natural question whether all Ramsey quantifiers are either polynomial-time computable or NP-hard, and whether we can give a natural characterization of the polynomial-time computable quantifiers. In this paper, we first show that there exist intermediate Ramsey quantifiers and then we prove a dichotomy result for a large and natural class of Ramsey quantifiers, based on a reasonable and widely-believed complexity assumption. We show that the polynomial-time computable quantifiers in this class are exactly the constant-log-bounded Ramsey quantifiers.
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