@conference {38,
	title = {Beyond Regularity for Presburger Modal Logics},
	booktitle = { 9th Workshop on Advances in Modal Logics (AiML{\textquoteright}12)},
	year = {2012},
	month = {08/2012},
	publisher = {College Publications},
	organization = {College Publications},
	address = {Copenhagen, Denmark},
	abstract = {Satisability problem for modal logic K with quantier-free Presburger and regularity constraints (EML) is known to be pspace-complete. In this paper, we consider its extension with nonregular constraints, and more specically those expressed by visibly pushdown languages (VPL). This class of languages behaves nicely, in particular when combined with Propositional Dynamic Logic (PDL). By extending EML, we show that decidability is preserved if we allow at most one positive VPL-constraint at each modal
depth. However, the presence of two VPL-contraints or the presence of a negative occurrence of a single VPL-constraint leads to undecidability. These results contrast with the decidability of PDL augmented with VPL-constraints.
Keywords: Presburger constraint, context-free constraint, decidability},
	keywords = {context-free constraint, decidability, Presburger constraint},
	url = {http://www.lsv.ens-cachan.fr/Publis/PAPERS/PDF/CD-aiml12.pdf},
	author = {Facundo Carreiro and St{\'e}phane Demri}
}