English

Alternating Set Quantifiers in Modal Logic

Logic in Computer Science 2016-03-01 v1 Formal Languages and Automata Theory Logic

Abstract

We establish the strictness of several set quantifier alternation hierarchies that are based on modal logic, evaluated on various classes of finite graphs. This extends to the modal setting a celebrated result of Matz, Schweikardt and Thomas (2002), which states that the analogous hierarchy of monadic second-order logic is strict. Thereby, the present paper settles a question raised by van Benthem (1983), revived by ten Cate (2006), and partially answered by Kuusisto (2008, 2015).

Keywords

Cite

@article{arxiv.1602.08971,
  title  = {Alternating Set Quantifiers in Modal Logic},
  author = {Fabian Reiter},
  journal= {arXiv preprint arXiv:1602.08971},
  year   = {2016}
}

Comments

20 pages, 2 figures; Can be seen as a follow-up paper to arXiv:1408.3030; Typeset using Linux Libertine as main font and AMS Euler as math font

R2 v1 2026-06-22T12:59:55.031Z