Model-theoretic and Computational Properties of Modal Dependence Logic

We study the basic modal language extended by an operator dep. If p
i
are propositional atoms, then dep(p
1
,…,p
n
−1
;p
n
) expresses, intuitively, that p
n
only depends on p
1
,…,p
n
−1
. The resulting language was baptized ‘modal dependence logic’ by Väänänen in his paper Modal Dependence Logic. The current article compares modal dependence logic with basic modal logic in terms of its model-theoretic and computational properties. We show that modal dependence logic is strictly more expressive than modal logic, but that under special conditions modal dependence logic can be translated into basic modal logic.We show that the complexity of modal dependence logic is NEXP-complete.