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Questions tagged [free-logic]

For questions about logic that do not require the objects in the domain of quantification to "exist". The adjective "free" is used in contrast to the adjective "classical".

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Does ◻(∀x)(Fx ⊃ ◻(E!x & (E!x ⊃ Fx))) entail ◻((∃x)Fx ⊃ ◻(∃x)Fx)?

I was wondering if we can derive ◻((∃x)Fx ⊃ ◻(∃x)Fx) from ◻(∀x)(Fx ⊃ ◻(E!x & (E!x ⊃ Fx)))? (By the way 'E!' is the existence predicate.) I am using the Quantified Free Modal Logic constructed/...
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What does “E!” mean in free logic?

Reading John Nolt's "Free Logic" article I see the symbol "E!" in the "2.1 Axiom Systems". The following axioms are special for free logics. (A4) ∀xA→(E!t→A(t/x)) (A5) ∀xE!x (A4) modifies ...