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  "body": "\n## Statement\n\nThe following table lists common modal axioms together with their corresponding classes. The naming of the axioms often varies; Here, axiom **K** is named after Saul Kripke; axiom **T** is named after the truth axiom in epistemic logic; axiom **D** is named after deontic logic; axiom **B** is named after L. E. J. Brouwer; and axioms **4** and **5** are named based on C. I. Lewis's numbering of symbolic logic systems.\n\nAxiom **K** can also be rewritten as $\\Box [(A\\to B)\\land A]\\to \\Box B$, which logically establishes [[modus ponens|0Y0MQYST0M]] as a rule of inference in every possible world.\n\nNote that for axiom **D**, $\\Diamond A$ implicitly implies $\\Diamond\\top$, which means that for every possible world in the model, there is always at least one possible world accessible from it (which could be itself). This implicit implication $\\Diamond A \\rightarrow \\Diamond\\top$ is similar to the implicit implication by [[existential quantifier on the range of quantification|0FYQMKFE77]].\n",
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