Extended Modal Dependence Logic $\mathcal{EMDL}$

Abstract

In this paper we extend modal dependence logic $\mathcal{MDL}$ by allowing dependence atoms of the form dep(ϕ ₁,…,ϕ _n ) where ϕ _i , 1 ≤ i ≤ n, are modal formulas (in $\mathcal{MDL}$, 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 $\mathcal{EMDL}$ strictly extends $\mathcal{MDL}$, i.e., there exist $\mathcal{EMDL}$-formulas which are not expressible in $\mathcal{MDL}$. 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 $\mathcal{EMDL}$ and $\mathcal{MDL}$ coincide. In addition we show that $\mathcal{EMDL}$ is equivalent to $\mathcal{ML}$ extended by a certain propositional connective.

This paper was supported by a grant from DAAD within the PPP programme under project ID 50740539 and grant 138163 of the Academy of Finland.