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20 Cards in this Set
- Front
- Back
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Quantifier of PL
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An expression of PL of the form (∀x) or (∃x).
(∀x) = Universal quantifier. (∃x) = Existential quantifier. |
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Sentence of PL
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A formula P of PL is a sentence of PL iff no occurrence of a variable in P is free.
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What is the contradictory of (∀x)(P⊃Q)?
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(∃x)(P & ~Q)
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What is the contradictory of (∀x)(P ⊃ ~Q)?
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(∃x) (P&Q)
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A
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(∀x) (P ⊃ Q)
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E
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(∀x) (P ⊃ ~Q)
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I
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(∃x) (P & Q)
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O
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(∃x) (P & ~Q)
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(∀y) (∀x) Lyx
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"Everyone likes everyone."
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(∃y) (∃x) Lyx
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"Someone likes someone."
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(∀x) (∃y) Lxy
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"Everyone likes someone."
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(Ey) (∀x) Lxy
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"Someone is liked by everyone."
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Quantificational Inconsistency
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Γ has a closed truth tree.
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Quantificational consistency
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Γ is not quantificationally inconsistent; if Γ does not have a closed truth tree.
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Quantificational truth
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The set [~P] has a closed truth tree.
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Quantificational Falsity
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The set [P] has a closed truth tree.
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Quantificational Indeterminacy
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Neither the set [P] nor the set [~P] has a closed truth tree.
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Quantificational Equivalence
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P and Q of PL/PLE are quantificationally equivalent iff the set [~(P≡Q)] has a closed truth tree.
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Quantificational Entailment
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Γ ∪ {~P} has a closed truth tree (Where Γ -a finite set- entails P -a sentence-)
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Quantificational validity
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An argument of PL/PLE with a finite number of premises is quantificationall valid iff the set consisting of the premises and the negation of the conclusion has a closed truth tree.
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