Modal logic
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Decidability of the Guarded Fragment with the Transitive Closure
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
A universally defined undecidable unimodal logic
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Two-Variable First-Order Logic with Equivalence Closure
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Hi-index | 0.00 |
In this paper, the modal logic over classes of structures definable by universal first-order Horn formulas is studied. We show that the satisfiability problems for that logics are decidable, confirming the conjecture from [E. Hemaspaandra and H. Schnoor, On the Complexity of Elementary Modal Logics, STACS 08]. We provide a full classification of logics defined by universal first-order Horn formulas, with respect to the complexity of satisfiability of modal logic over the classes of frames they define. It appears, that except for the trivial case of inconsistent formulas for which the problem is in P, local satisfiability is either NP-complete or PSPACE-complete, and global satisfiability is NP-complete, PSPACE-complete, or EXPTIME-complete. While our results holds even if we allow to use equality, we show that inequality leads to undecidability.