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It is not the case that KQML is not the uniquely correct modal quantified logic; stronger systems like SQML with fixed domains make Box-N a logical truth.
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Reasons For
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Reason for
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1.
Fixed domain assumptions are metaphysically controversial; they may rule out plausible scenarios like contingent existence without philosophical warrant.
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2.
A theorem being derivable in SQML doesn't make it a logical truth unless SQML's axioms capture the correct modal logic—which remains contested.
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3.
KQML's flexibility better matches ordinary language where we quantify over what actually exists, not across all possible worlds.
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Reasons Against
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Reason against
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1.
Fixed domain systems eliminate the philosophical problem of objects existing in some possible worlds but not others, making necessity claims more coherent.
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2.
SQML's Box-N theorem follows logically from its axioms; if the axioms are justified, the theorem's truth is not optional.
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3.
KQML's variable domain semantics creates counterintuitive results where the same formula can shift truth-value based on domain changes across worlds.
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