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  1. Modal Languages and Bounded Fragments of Predicate Logic.Hajnal Andréka, István Németi & Johan van Benthem - 1998 - Journal of Philosophical Logic 27 (3):217 - 274.
    What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...)
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