Abstract
Intuitionistic modal logics originate from different sources and have different areas of application. They include philosophy (see, e.g., Prior (1957), Ewald (1986), Williamson (1992)), the foundations of mathematics (Kuznetsov, 1985, Kuznetsov and Muravitskij, 1986), and computer science (Plotkin and Stirling, 1986, Stirling, 1987, Wijesekera, 1990). Modalities are added to intuitionistic logic in the framework of studying “new intuitionistic connectives” (Bessonov, 1977, Gabbay, 1977, Yashin, 1994) and to simulate the monadic fragment of intuitionistic first order logic (Bull, 1966, Ono, 1977, Ono and Suzuki, 1988, Bezhanishvili, 1997). The multitude of constructed logics was examined “piecewise”, often by means of creating a special semantical and syntactical apparatus. A broader perspective is to try combining the well-developed general theories of classical modal logics and nonmodal superintuitionistic (alias intermediate) logics in order to embrace the classes of extensions of some reasonable basic modal systems on the intuitionistic base.
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Wolter, F., Zakharyaschev, M. (1999). Intuitionistic Modal Logic. In: Cantini, A., Casari, E., Minari, P. (eds) Logic and Foundations of Mathematics. Synthese Library, vol 280. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2109-7_17
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