International Workshop on Logic, Language, Information, and Computation

WoLLIC 2015: Logic, Language, Information, and Computation pp 69-80

A Dichotomy Result for Ramsey Quantifiers

Conference paper

DOI: 10.1007/978-3-662-47709-0_6

Volume 9160 of the book series Lecture Notes in Computer Science (LNCS)
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

Abstract

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Algorithms and Complexity GroupVienna University of TechnologyViennaAustria
  2. 2.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands