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Dependence logic with a majority quantifier

Authors Arnaud Durand, Johannes Ebbing, Juha Kontinen, Heribert Vollmer



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Arnaud Durand
Johannes Ebbing
Juha Kontinen
Heribert Vollmer

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Arnaud Durand, Johannes Ebbing, Juha Kontinen, and Heribert Vollmer. Dependence logic with a majority quantifier. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 252-263, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)
https://doi.org/10.4230/LIPIcs.FSTTCS.2011.252

Abstract

We study the extension of dependence logic D by a majority quantifier M over finite structures. We show that the resulting logic is equi-expressive with the extension of second-order logic by second-order majority quantifiers of all arities. Our results imply that, from the point of view of descriptive complexity theory, D(M) captures the complexity class counting hierarchy.
Keywords
  • dependence logic
  • counting hierarchy
  • majority quantifier
  • second order logic
  • descriptive complexity
  • finite model theory

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