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20 Cards in this Set

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