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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Questions on Precise Meaning of Quine's Ontological Commitment Criterion

In a recent paper Ontological Commitment, Augustin Rayo tries to make the notion of ontological commitment more precise. He specifies: "Quine’s Criterion (Logical Version) A first-order ...
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Variant of free logic that accepts domain emptiness but rejects non-referring terms

To my naive perspective, domains that might be empty and terms that fail to denote (via constant symbols that don't refer or partial functions) feel radically different. The former seems ordinary and ...
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Does ◻(∀x)[Px ≡ ◻(E!x → Qx)] and ◻(∀x)(Qx → ◻E!x) entail ◻(∀x){Px ≡ ◻[E!x & (E!x → Qx)]}?

Say we are working in a free quantified modal logic system S5. Would the following argument be valid: ◻(∀x)[Px ≡ ◻(E!x → Qx)] (Premise) ◻(∀x)(Qx → ◻E!x) (Premise) ◻(∀x){Px ≡ ◻[E!x & (E!x → Qx)]}...
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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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1answer
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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) ...