Calcul Propositionnel

(P∨Q)∧P(P∧Q)∨P
P∨(Q∧R)≡(P∨Q)∧(P∨R)
P∧(Q∨R)≡(P∧Q)∨(P∧R)
{p∨q∨ ¬r, ¬p∨q∨ ¬r, p ∨ ¬q∨r}
{p⇒q⇒p, r ⇒(r⇒⊥)⇒p, (p⇒q⇒r)⇒(p⇒q)⇒p⇒r}
{p⇒q, (p⇒¬q⇒r)⇒r, ¬r}
φ(P)P
φ(P)P φ(>)φ(⊥)
A φ(A)
φ(¬A)
A B φ(A)φ(B)
φ(A∧B)φ(A∨B)φ(A⇒B)
P∈φ(P)
(P) = 0 P
(¬P) = 1 + (P)
(P◦Q) = 1 + (P) + (Q)◦ ∈ {∨,∧,⇒}
φ n P
(P)≤n φ(P)
φ(P)P
a
(>) = a∨ ¬a
(⊥) = ¬(a∨ ¬a)
(p) = p p
(¬P) = ¬( (P))
(P∧Q) = ¬(¬(P)∨ ¬ (Q))
(P∨Q) = (P)∨(Q)
(P⇒Q) = ¬(P)∨(Q)

(P)P
P
Q P Q =P
Q P P =¬P0Q P 0
P=P1◦P2Q P1P2◦
{∨,∧,⇒,⇔}
¬(p∨(q∧r))⇒(p∧q)
→℘( )
P
P n
xx x
x x
P x
x,P x,P x P
x
2p q
p q
n