On the decidability of elementary modal logics Journal Article


Author(s): Michaliszyn, Jakub; Otop, Jan; Kieroňski, Emanuel
Article Title: On the decidability of elementary modal logics
Affiliation IST Austria
Abstract: We consider the satisfiability problem for modal logic over first-order definable classes of frames.We confirm the conjecture from Hemaspaandra and Schnoor [2008] that modal logic is decidable over classes definable by universal Horn formulae. We provide a full classification of Horn formulae with respect to the complexity of the corresponding satisfiability problem. It turns out, that except for the trivial case of inconsistent formulae, local satisfiability is eitherNP-complete or PSPACE-complete, and global satisfiability is NP-complete, PSPACE-complete, or ExpTime-complete. We also show that the finite satisfiability problem for modal logic over Horn definable classes of frames is decidable. On the negative side, we show undecidability of two related problems. First, we exhibit a simple universal three-variable formula defining the class of frames over which modal logic is undecidable. Second, we consider the satisfiability problem of bimodal logic over Horn definable classes of frames, and also present a formula leading to undecidability.
Keywords: computational complexity; Modal logic; Elementary logics
Journal Title: ACM Transactions on Computational Logic (TOCL)
Volume: 17
Issue 1
ISSN: 1557-945X
Publisher: ACM  
Date Published: 2015-09-01
Start Page: Article number: 2
DOI: 10.1145/2817825
Open access: no
IST Austria Authors
  1. Jan Otop
    16 Otop
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