Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic
DOI:
https://doi.org/10.18778/0138-0680.48.3.03Keywords:
intuitionistic modal logic, neighbourhood semantics, topological semantics, Kripke frames, soundness and completenessAbstract
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.
References
M. Božic, K. Došen, Models for normal intuitionistic modal logics, Studia Logica, Vol. XLIII (1984).
Á. Császár, Generalized topology, generalized continuity, Acta Mathematica Hungarica, Vol. 96, No. 4 (2002), pp. 351–357.
M. J. Collinson, B. P. Hilken, D. E. Rydeheard, An adjoint construction for topological models of intuitionistic modal logic. Extended abstract, http://sierra.nmsu.edu/morandi/old%20files/TbilisiConference/Collinson.pdf
J. M. Davoren, Topological Semantics and Bisimulations for Intuitionistic Modal Logics and Their Classical Companion Logics, Logical Foundations of Computer Science 2007, Springer 2007.
J. M. Davoren, V. Coulthard, T. Moor, R. P. Goré, A. Nerode, On Intuitionistic Modal and Tense Logics and Their Classical Companion Logics: Topological Semantics and Bisimulations, Annals of Pure and Applied Logic, Vol. 161 (2009), pp. 349–367.
J. M. Davoren, V. Coulthard, T. Moor, R. P. Goré, A. Nerode, Topological semantics for Intuitionistic modal logics and spatial discretisation by A/D maps, [in:] Workshop on Intuitionistic Modal Logic and Applications (IMLA), Copenhagen, Denmark 2002.
D. de Jongh, F. Sh. Maleki, Two neighborhood semantics for subintuitionistic logics, http://events.illc.uva.nl/Tbilisi/Tbilisi2017/uploaded_files/inlineitem/Dick_de_Jongh_Fateme_Shirmohammadzadeh_Maleki.pdf
D. de Jongh, F. Sh. Maleki, Weak subintuitionistic logics, https://www.illc.uva.nl/Research/Publications/Reports/PP-2016-12.text.pdf
M. Moniri, F. S. Maleki, Neighborhood semantics for basic and intuitionistic logic, Logic and Logical Philosophy, Vol. 23 (2015), pp. 339–355.
E. Pacuit, Neighborhood Semantics for Modal Logic, Springer International Publishing AG 2017.
V. H. Sotirov, Modal Theories with Intuitionistic Logic, [in:] Mathematical Logic, Proceedings of the Conference on Mathematical Logic, Dedicated to the Memory of A. A. Markov (1903–1979), September 22–23, 1980, pp. 139–171, Sofia 1984.
T. Speer, A Short Study of Alexandroff Spaces, https://arxiv.org/pdf/0708.2136.pdf
T. Witczak, Generalized Topological Semantics for Weak Modal Logics, https://arxiv.org/pdf/1904.06099.pdf
T. Witczak, Intuitionistic Modal Logic Based on Neighborhood Semantics Without Superset Axiom, https://arxiv.org/pdf/1707.03859.pdf
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
How to Cite
