thodg/slides

diff --git a/modal-logic/index.md b/modal-logic/index.md
index 145870b..df25f1f 100644
--- a/modal-logic/index.md
+++ b/modal-logic/index.md
@@ -1,13 +1,46 @@
 # Modal logic
 
 ## 1. Notation
-¬A   "Not A"
 
-□A    "It is necessary that A"
+### 1.1 Not
+"Not A"
 
-◊A    "It is possible that A"
+¬A
 
-A → B "If A then B"
+### 1.2 Necessarilly
+"It is necessary that A"
+
+□A
+
+### 1.3 Possibly
+"It is possible that A"
+
+◊A
+
+### 1.4 Implies
+"If A then B"
+
+A → B
+
+### 1.5 Conjunction
+"A and B"
+
+A ∧ B
+
+### 1.6 Disjunction
+"A or B"
+
+A ∨ B
+
+### 1.7 Exclusive disjunction
+"A xor B"
+
+A ⊕ B
+
+### 1.8 Mutual implication
+"If A then B and if B then A"
+
+A ↔ B
 
 ## 2. Contruction
 K is a weak logic (Saul Kripke)
@@ -21,7 +54,15 @@ A is a theorem of K → □A is a theorem of K
 ### 2.3 Operator ◊
 ◊A = ¬□¬A
 
-## 3. T
+## 3. Lemmas
+
+### 3.1 Necessary conjunction
+□(A ∧ B) ↔ □A ∧ □B
+
+### 3.2 Disjonction of necessities
+◻A ∨ ◻B → □(A ∨ B)
+
+## 4. T
 T is K plus the following axiom :
 
 □A → A