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.
A dichotomy result for ramsey quantifiers / De Haan, Ronald; Szymanik, Jakub. - 9160:(2015), pp. 69-80. ( 22nd International Workshop on Logic, Language, Information and Computation, WoLLIC 2015 Bloomington 2015) [10.1007/978-3-662-47709-0_6].
A dichotomy result for ramsey quantifiers
Szymanik, Jakub
2015-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
