Model checking for modal intuitionistic dependence logic

Authors:
Johannes Ebbing;Peter Lohmann;Fan Yang
Affiliations:
Theoretical Computer Science, Leibniz University Hannover, Hannover, Germany;Theoretical Computer Science, Leibniz University Hannover, Hannover, Germany;Department of Mathematics and Statistics, University of Helsinki, Finland
Venue:
TbiLLC'11 Proceedings of the 9th international conference on Logic, Language, and Computation
Year:
2011

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Abstract

Modal intuitionistic dependence logic ($\mathcal MIDL $) incorporates the notion of "dependence" between propositions into the usual modal logic and has connectives which correspond to intuitionistic connectives in a certain sense. It is the modal version of a variant of first-order dependence logic (Väänänen 2007) considered by Abramsky and Väänänen (2009) basing on Hodges' team semantics (1997). In this paper, we study the computational complexity of the model checking problem for $\mathcal MIDL$ and its fragments built by restricting the operators allowed in the logics. In particular, we show that the model checking problem for $\mathcal MIDL$ in general is PSPACE-complete and that for propositional intuitionistic dependence logic is coNP-complete.