Characterizing definability of second-order generalized quantifiers

Authors:
Juha Kontinen;Jakub Szymanik
Affiliations:
Department of Mathematics and Statistics, University of Helsinki;Institute of Artificial Intelligence, University of Groningen
Venue:
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
Year:
2011

Citing 11
Cited 0

Algebraic methods in the theory of lower bounds for Boolean circuit complexity

STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Parallel computation with threshold functions

Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
On uniformity within NC1

Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
A uniform approach to define complexity classes

Theoretical Computer Science
Uniform constant-depth threshold circuits for division and iterated multiplication

Journal of Computer and System Sciences - Complexity 2001
Generalized Quantifiers, an Introduction

ESSLLI '97 Revised Lectures from the 9th European Summer School on Logic, Language, and Information: Generalized Quantifiers and Computation
A Generalization of the Büchi-Elgot-Trakhtenbrot Theorem

CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
First-order expressibility of languages with neutral letters or: The Crane Beach conjecture

Journal of Computer and System Sciences
A Remark on Collective Quantification

Journal of Logic, Language and Information
A logical characterization of the counting hierarchy

ACM Transactions on Computational Logic (TOCL)
Extensions of MSO and the monadic counting hierarchy

Information and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier Q1 is definable in terms of another quantifier Q2, the base logic being monadic second-order logic, reduces to the question if a quantifier Q1* is definable in FO(Q2*, *1 and Q2*. We use our characterization to show new definability and nondefinability results for second-order generalized quantifiers. In particular, we show that the monadic second-order majority quantifier Most is not definable in second-order logic.