Alternating Set Quantifiers in Modal 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).

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