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.

中文翻译：

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表征多项式 Ramsey 量词

Ramsey 量词不仅是逻辑和计算机科学的自然研究对象，也是自然语言的形式语义学的自然研究对象。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 Ramsey 量词都是多项式时间可计算的还是 NP 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，我们首先证明存在中间 Ramsey 量词，然后我们基于合理且广泛相信的复杂性假设证明了大量自然类别的 Ramsey 量词的二分结果。我们表明此类中的多项式时间可计算量词正是常数对数有界拉姆齐量词。