modal logic
Noun
Meaning
a system of logic whose formal properties resemble certain moral and epistemological concepts
the logical study of necessity and possibility
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Besides axiom 1-5 and definition 1-3, a few other axioms from modal logic were tacitly used in the proof.
For any class C of Kripke frames, Thm(C) is a normal modal logic (in particular, theorems of the minimal normal modal logic, K, are valid in every Kripke model).
However, relatively few systems of modal logic can be formalised directly in natural deduction.
In some cases, we can use FMP to prove Kripke completeness of a logic: every normal modal logic is complete wrt a class of modal algebras, and a finite modal algebra can be transformed into a Kripke frame.
In the most common semantics for modal logic, many " possible worlds " are considered.
Intuitionistic logic Kripke semantics for the intuitionistic logic follows the same principles as the semantics of modal logic, but uses a different definition of satisfaction.