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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Presburger Modal Logic Is PSPACE-Complete
verfasst von : Stéphane Demri, Denis Lugiez
Erschienen in: Automated Reasoning
Verlag: Springer Berlin Heidelberg
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We introduce a Presburger modal logic PML with regularity constraints and full Presburger constraints on the number of children that generalize graded modalities, also known as number restrictions in description logics. We show that PML satisfiability is only pspace-complete by designing a Ladner-like algorithm that can be turned into an analytic proof system. algorithm. This extends a well-known and non-trivial pspace upper bound for graded modal logic. Furthermore, we provide a detailed comparison with logics that contain Presburger constraints and that are dedicated to query XML documents. As an application, we show that satisfiability for Sheaves Logic SL is pspace-complete, improving significantly its best known upper bound.