On the modal $μ$-calculus over finite symmetric graphs

Year, pages: 2015, 731 - 746

In this paper we consider the alternation hierarchy of the modal $μ$-calculus over finite symmetric graphs and show that in this class the hierarchy is infinite. The $μ$-calculus over the symmetric class does not enjoy the finite model property, hence this result is not a trivial consequence of the strictness of the hierarchy over symmetric graphs. We also find a lower bound and an upper bound for the satisfiability problem of the $μ$-calculus over finite symmetric graphs.

D'agostino, G., Lenzi, G. 2015. On the modal $μ$-calculus over finite symmetric graphs. In Mathematica Slovaca, vol. 65, no.4, pp. 731-746. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0052

D'agostino, G., Lenzi, G. (2015). On the modal $μ$-calculus over finite symmetric graphs. Mathematica Slovaca, 65(4), 731-746. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0052