S. Baratella and A. Masini. A way of making intensional quantification explicit. Logic Journal of the IGPL, 2004.

We introduce the intensional logic IQL whose main feature is the capability of recovering modal operator Box by means of a genuine first-order quantification over worlds and of an intensional operator (the two components behaving independently). We prove that IQL is sound and complete with respect to an adequate class of structures and that it is decidable. We further show that IQL is a conservative extension of modal system K and of monadic predicate calculus up to interpretability. Eventually we introduce a simple proof system in natural deduction style for IQL

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