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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.
