A Dichotomy Result for Ramsey Quantifiers
- Cite this paper as:
- de Haan R., Szymanik J. (2015) A Dichotomy Result for Ramsey Quantifiers. In: de Paiva V., de Queiroz R., Moss L., Leivant D., de Oliveira A. (eds) Logic, Language, Information, and Computation. WoLLIC 2015. Lecture Notes in Computer Science, vol 9160. Springer, Berlin, Heidelberg
Ramsey quantifiers are a natural object of study not only for logic and computer science, but also for 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.