The complexity of existential quantification in concept languages
Artificial Intelligence
Dependence Logic: A New Approach to Independence Friendly Logic (London Mathematical Society Student Texts)
The Complexity of Satisfiability for Fragments of CTL and CTL*;
Electronic Notes in Theoretical Computer Science (ENTCS)
Model-theoretic and Computational Properties of Modal Dependence Logic
Journal of Logic and Computation
The Complexity of Problems for Quantified Constraints
Theory of Computing Systems
Generalized modal satisfiability
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Complexity of model checking for modal dependence logic
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Model checking for modal intuitionistic dependence logic
TbiLLC'11 Proceedings of the 9th international conference on Logic, Language, and Computation
Complexity Results for Modal Dependence Logic
Studia Logica
The Dynamification of Modal Dependence Logic
Journal of Logic, Language and Information
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Modal dependence logic was introduced very recently by Väänänen. It enhances the basic modal language by an operator dep. For propositional variables p1, ..., pn, dep(p1, ..., pn-1; pn) intuitively states that the value of pn only depends on those of p1, ..., pn-1. Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time. In this paper we consider fragments of modal dependence logic obtained by restricting the set of allowed propositional connectives. We show that satisfibility for poor man's dependence logic, the language consisting of formulas built from literals and dependence atoms using ∧, □, ⋄ (i. e., disallowing disjunction), remains NEXPTIME-complete. If we only allow monotone formulas (without negation, but with disjunction), the complexity drops to PSPACE-completeness. We also extend Väänänen's language by allowing classical disjunction besides dependence disjunction and show that the satisfiability problem remains NEXPTIME-complete. If we then disallow both negation and dependence disjunction, satistiability is complete for the second level of the polynomial hierarchy. In this way we completely classifiy the computational complexity of the satisfiability problem for all restrictions of propositional and dependence operators considered by Väänänen and Sevenster.