Editing Modal logic (section)

== Extensions ==
Modal logics may be extended to [[fuzzy logic|fuzzy form]] with calculi in the class of fuzzy Kripke models.<ref>A. M. Mironov, "Fuzzy Modal Logics" [[Journal of Mathematical Sciences]], Springer, Volume 128, pages 3461–3483, (2005) [https://link.springer.com/article/10.1007/s10958-005-0281-1]</ref>

Modal logics may also be enhanced via ''base-extension semantics'' for the classical propositional systems. In this case, the validity of a formula can be shown by an inductive definition generated by provability in a ‘base’ of atomic rules.<ref>Timo Eckhardt and  David Pym "Base-extension semantics for modal logic" [[Logic Journal of the IGPL]] Volume 33, Issue 2, April 2025</ref>
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[[Intuitionistic logic|Intuitionistic]] modal logics are used in different areas of application, and they have often risen from different sources. The areas include the foundations of mathematics, computer science and philosophy. In these approaches, often modalities are added to intuitionistic logic to create new intuitionistic connectives and to simulate the monadic elements of intuitionistic [[first order logic]].<ref>F. Wolter et al "Intuitionistic Modal Logic" in Logic and Foundations of Mathematics, Sppringer 1999, pp 227-238</ref>