My old paper on the intuitionistic modal logics is accessible
here. It recapitulates the main results of my Ph.D. thesis (Moscow State
University, 1978). A few misprints have been corrected (published in:
Mathematical Logic, Proc. Conf. Math. Logic Dedicated to the Memory of A. A.
Markov (1903 - 1979), Sofia, September 22 - 23, 1980. Sofia, 1984, pp.
139-171):
Modal
Theories with Intuitionistic Logic
As we know, any extension of Dummett's intermediate logic is tabular and therefore has the finite model property (f.m.p.). I built a modal extension of Dummett's logic which lacks the f.m.p. Something more, on all finite models, my system is modal only fictiously. That is, its proper modal theorems can be distinguished using infinite models only. See the
details (in Russian: Matematicheskie
zametki, 27 (1980), no. 1, pp. 89-94; in English: Mathematical
Notes of the Academy of Sciences of the USSR, 27(1980), no. 1,
pp. 47-49):
Nonfinitely Approximable Intuitionistic Modal Logics
Here is the first axiomatization of the intuitionistic double negation
considered as a kind of intuitionistic necessity (VII
Intern. Wittgenstein Symp., Kirchberg am Wechsel, August 22-29, 1982, Summaries,
p. 58.):
The Intuitionistic Double Negation Is a Modality
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