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Complexity of Polyadic Quantifiers

  • Jakub SzymanikEmail author
Chapter
Part of the Studies in Linguistics and Philosophy book series (SLAP, volume 96)

Abstract

In this chapter, rather mathematical in nature, I provide a top-down computational perspective on polyadic quantification in natural language, that is, starting with a general computational model of Turing machines I investigate complexity differences between various polyadic constructions. I propose a classification of natural language polyadic quantifiers with respect to their computational complexity, especially focusing on the border between tractable and intractable constructions. First, I prove that iteration, cumulation, and resumption do not carry us outside polynomial computability. Other polyadic construction, like branching and Ramseyification, can lead to NP-complete natural language constructions. In the last section of this chapter-motivated by the search for noncontroversial intractable semantic constructions-I investigate the computational complexity duality between Ramsey quantifiers: some are in P while others are NP-complete. Ramsey quantifiers are a natural object of study not only for logic and computer science, but also, as I will show in the next chapter, for formal semantics of natural language.

Keywords

Descriptive computational complexity Second-order logic  Model-checking Polyadic quantifiers Branching (Henkin) quantifiers Ramsey quantifiers Boundness NP-intermediate Computational dichotomy 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

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