Beyond Regularity for Presburger Modal Logics

TitleBeyond Regularity for Presburger Modal Logics
Publication TypeConference Paper
Year of Publication2012
AuthorsCarreiro, F, Demri, S
Conference Name 9th Workshop on Advances in Modal Logics (AiML'12)
Date Published08/2012
PublisherCollege Publications
Conference LocationCopenhagen, Denmark
Keywordscontext-free constraint, decidability, Presburger constraint
AbstractSatis 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
Refereed DesignationRefereed
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