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  "body": "\n## Statement\n\nThe following makes use of the modal operators $\\Box$ (\"necessarily\") and $\\Diamond$ (\"possibly\").\n\nS5 is characterized by the axioms:\n\n- **K**: $\\Box(A\\to B)\\to(\\Box A\\to\\Box B)$;\n- **T**: $\\Box A \\to A$,\n\nand either:\n\n- **5**: $\\Diamond A\\to \\Box\\Diamond A$;\n- or both of the following:\n  - **4**: $\\Box A\\to\\Box\\Box A$, and\n  - **B**: $A\\to\\Box\\Diamond A$.\n\nThe (5) axiom restricts the accessibility relation $R$ of the Kripke frame to be Euclidean, i.e. $(wRv \\land wRu) \\implies vRu$, thereby conflating necessity with possibility under idempotence.\n",
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