If necessitism is correct, the invalidity of BF in KQML's semantics indicates a defect in that semantics' metaphysical adequacy, not a proof of BF's unprovability in all legitimate modal logics.
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The quality of a statement that cannot be logically proven true using the accepted rules and facts of a system, like a math problem that has no solution.
Validity (in logic)(what the tests are trying to determine about logical formulas)
Whether a logical statement or argument follows the rules correctly and must be true if its assumptions are true.
necessitism(Philosophy of modality; a logical truth of SQML)
The view that everything that exists exists necessarily — both possibilia and actually existing things alike are necessary beings, such that there are no worlds from which they are altogether absent.