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Extended Modal Dependence Logic EMDL

In this paper we extend modal dependence logic MDL by allowing dependence atoms of the form dep(φ1, . . . , φn) where φi, 1 ≤ i ≤ n, are modal formulas (in MDL, only propositional variables are allowed in dependence atoms). The reasoning behind this extension is that it introduces a temporal component into modal dependence logic. E.g., it allows us to express that truth of propositions in some world of a Kripke structure depends only on a certain part of its past. We show that EMDL strictly extends MDL, i.e., there exist EMDL-formulas which are not expressible in MDL. However, from an algorithmic point of view we do not have to pay for this since we prove that the complexity of satisfiability and model checking of EMDL and MDL coincide. In addition we show that EMDL is equivalent to ML extended by a certain propositional connective.