Computational Aspects of Dependence Logic

In this thesis (modal) dependence logic is investigated. It was introduced in 2007 by Jouko Väänänen as an extension of first-order (resp. modal) logic by the dependence operator “p ̈q. For first-order (resp. propositional) variables x1, . . . , xn, “px1, . . . , xn ́1, xnq intuitively states that the value of xn is determined by those of x1, . . . , xn ́1. We consider fragments of modal dependence logic obtained by restricting the set of allowed modal and propositional connectives. We classify these fragments with respect to the complexity of their satisfiability and modelchecking problems. For satisfiability we obtain complexity degrees from P over NP, Σ2 and PSPACE up to NEXP, while for model-checking we only classify the fragments with respect to their tractability, i. e. we either show NP-completeness or containment in P. We then study the extension of modal dependence logic by intuitionistic implication. For this extension we again classify the complexity of the modelchecking problem for its fragments. Here we obtain complexity degrees from P over NP and coNP up to PSPACE. Finally, we analyze first-order dependence logic, independence-friendly logic and their two-variable fragments. We prove that satisfiability for twovariable dependence logic is NEXP-complete, whereas for two-variable independence-friendly logic it is undecidable; and use this to prove that the latter is also more expressive than the former.