Hash :
955b1103
Author :
Thomas de Grivel
Date :
2020-05-17T12:14:58
modal logic
¬A “Not A”
□A “It is necessary that A”
◊A “It is possible that A”
A → B “If A then B”
K is a weak logic (Saul Kripke)
A is a theorem of K → □A is a theorem of K
□(A → B) → (□A → □B)
T is K plus the following axiom :
□A → A
# Modal logic
## 1. Notation
¬A "Not A"
□A "It is necessary that A"
◊A "It is possible that A"
A → B "If A then B"
## 2. Contruction
K is a weak logic (Saul Kripke)
### 2.1 Necessitation rule
A is a theorem of K → □A is a theorem of K
### 2.2 Distribution axiom
□(A → B) → (□A → □B)
## 3. T
T is K plus the following axiom :
□A → A