Alternating Set Quantifiers in Modal Logic [article]

Fabian Reiter
2016 arXiv   pre-print
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).
arXiv:1602.08971v1 fatcat:sum4d4tp5zhwvjsafg4oh2zfwm