Geodesic
Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic
Bulletin of the Section of Logic, Tome 48 (2019) no. 3, pp. 187-205

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We present three examples of topological semantics for intuitionistic modal logic with one modal operator □. We show that it is possible to treat neighborhood models, introduced earlier, as topological or multi-topological. From the neighborhood point of view, our method is based on differences between properties of minimal and maximal neighborhoods. Also we propose transformation of multitopological spaces into the neighborhood structures.
Keywords: intuitionistic modal logic, neighbourhood semantics, topological semantics, Kripke frames, soundness and completeness 
@article{BSL_2019_48_3_a2,
     author = {Witczak, Tomasz},
     title = {Topological and {Multi-Topological} {Frames} in the {Context} of {Intuitionistic} {Modal} {Logic}},
     journal = {Bulletin of the Section of Logic},
     pages = {187--205},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2019_48_3_a2/}
}
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Witczak, Tomasz. Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic. Bulletin of the Section of Logic, Tome 48 (2019) no. 3, pp. 187-205. http://geodesic.mathdoc.fr/item/BSL_2019_48_3_a2/