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I have been attempting to come to grips with Max Cresswell's account of this in Journal of Philosophical Logic 24 (4):379 - 403 (1995) where he presents proofs of the incompleteness of QK.2BF as well as QS4.2BF. I have difficulties accepting the accounts as there to my mind are some problems in the presentation.

(1) Are there more streamlined and convincing accounts in the literature on this topic which some could guide me to? (2) Have some studied adjusted notions of completeness according to which QS4.2BF and QK.2BF $\textbf{are}$ complete?

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    $\begingroup$ For (2), try Goldblatt’s book “Quantifiers, Propositions, and Identity: Admissible Semantics for Quantified Modal and Substructural Logics”. $\endgroup$
    – Emil Jeřábek
    Mar 15, 2014 at 21:59
  • $\begingroup$ Thanks for that Emil. I tried my university library at UiO for that book, but the organization of the electronic academic library resources is regrettably not yet good enough. Meanwhile I have been looking at A General Semantics for Quantified Modal Logic Robert Goldblatt and Edwin D. Mares $\endgroup$
    – Frode Alfson Bjørdal
    Mar 15, 2014 at 22:03

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