CM1 Flashcards

1
Q

LJ ax

A

________
Γ, A ⊢ A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

LK ax

A

________
Γ, A ⊢ Δ, A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

LJ cont

A

Γ, A, A ⊢ Δ
____________
Γ, A ⊢ Δ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

LK contright

A

Γ ⊢ Δ, A, A
____________
Γ ⊢ Δ, A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

LK contleft

A

Γ, A, A ⊢ Δ
____________
Γ, A ⊢ Δ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

LJ ⊤right

A

_______
Γ ⊢ ⊤

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

LK ⊤right

A

_______
Γ ⊢ Δ, ⊤

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

LJ ⊥left

A

_________
Γ, ⊥ ⊢ Δ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

LK ⊥left

A

_________
Γ, ⊥ ⊢ Δ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

LJ ¬right

A

Γ, A ⊢
________
Γ ⊢ ¬A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

LK ¬right

A

Γ, A ⊢ Δ
________
Γ ⊢ Δ, ¬A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

LJ ¬left

A

Γ ⊢ A
__________
Γ, ¬A ⊢ Δ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

LK ¬left

A

Γ ⊢ A, Δ
__________
Γ, ¬A ⊢ Δ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

LJ ∧right

A

Γ ⊢ A | Γ ⊢ B
________________
Γ ⊢ A ∧ B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

LK ∧right

A

Γ ⊢ Δ, A | Γ ⊢ Δ, B
________________
Γ ⊢ Δ, A ∧ B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

LJ ∧left

A

Γ, A, B ⊢ Δ
_______________
Γ, A ∧ B ⊢ Δ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

LK ∧left

A

Γ, A, B ⊢ Δ
_______________
Γ, A ∧ B ⊢ Δ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

LJ ∨right1

A

Γ ⊢ A
___________
Γ ⊢ A ∨ B

19
Q

LJ ∨right2

A

Γ ⊢ B
___________
Γ ⊢ A ∨ B

20
Q

LK ∨right

A

Γ ⊢Δ, A
___________
Γ ⊢ Δ, A ∨ B

21
Q

LJ ∨left

A

Γ, A ⊢ Δ | Γ, B ⊢ Δ
______________________
Γ, A ∨ B ⊢ Δ

22
Q

LK ∨left

A

Γ, A ⊢ Δ | Γ, B ⊢ Δ
______________________
Γ, A ∨ B ⊢ Δ

23
Q

LJ ⇒right

A

Γ, A ⊢ B
___________
Γ ⊢ A ⇒ B

24
Q

LK ⇒right

A

Γ, A ⊢ Δ, B
_____________
Γ ⊢ Δ, A ⇒ B

25
Q

LJ ⇒left

A

Γ ⊢ A | Γ, B ⊢ Δ
___________________
Γ, A ⇒ B ⊢ Δ

26
Q

LK ⇒left

A

Γ ⊢ Δ, A | Γ, B ⊢ Δ
___________________
Γ, A ⇒ B ⊢ Δ

27
Q

LJ ⇔right

A

Γ, A ⊢ B | Γ, B ⊢ A
_____________________
Γ ⊢ A ⇔ B

28
Q

LK ⇔right

A

Γ, A ⊢ Δ, B | Γ, B ⊢ Δ, A
_________________________
Γ ⊢ Δ, A ⇔ B

29
Q

LJ ⇔left1

A

Γ ⊢ A | Γ, B ⊢ Δ
__________________
Γ, A ⇔ B ⊢ Δ

30
Q

LJ ⇔left2

A

Γ ⊢ B | Γ, A ⊢ Δ
__________________
Γ, A ⇔ B ⊢ Δ

31
Q

LK ⇔left

A

Γ ⊢ Δ, A, B | Γ, A, B ⊢ Δ
_________________________
Γ, A ⇔ B ⊢ Δ

32
Q

LJ ∀right, x !∈ Γ

A

Γ ⊢ A(x)
_____________
Γ ⊢ ∀x. A(x)

33
Q

LK ∀right, x !∈ Γ, Δ

A

Γ ⊢ Δ, A(x)
_____________
Γ ⊢ Δ, ∀x. A(x)

34
Q

LJ ∀left

A

Γ, A(t) ⊢ Δ
_______________
Γ, ∀x. A(x) ⊢ Δ

35
Q

LK ∀left

A

Γ, A(t) ⊢ Δ
_______________
Γ, ∀x. A(x) ⊢ Δ

36
Q

LJ ∃right

A

Γ ⊢ A(t)
____________
Γ ⊢ ∃x. A(x)

37
Q

LK ∃right

A

Γ ⊢ Δ, A(t)
____________
Γ ⊢ Δ, ∃x. A(x)

38
Q

LJ ∃left, x !∈Γ, Δ

A

Γ, A(x) ⊢ Δ
_______________
Γ, ∃x. A(x) ⊢ Δ

39
Q

LK ∃left, x !∈Γ, Δ

A

Γ, A(x) ⊢ Δ
_______________
Γ, ∃x. A(x) ⊢ Δ

40
Q

LJ cut

A

Γ ⊢ A | Γ, A ⊢ B
_________________
Γ ⊢ B

41
Q

LK cut

A

Γ ⊢ Δ, A | Γ, A ⊢ Δ, B
_________________
Γ ⊢ Δ, B

42
Q

LJem em

A

Γ ⊢ ¬¬A
_________
Γ ⊢ A

43
Q

Quelles priorité appliquer sur les règles ?

A

Appliquer d’abord les opérateurs qui ne branches pas et les quantificateurs qui skolémisent

44
Q

Théorème de Herbrand

A

En logique classique, ∃x.P(x) ≡ il existe n termes t1, t2, . . ., tn tels que P(t1) ∨ P(t2) ∨ . . . ∨ P(tn) est vraie