thodg/slides/modal-logic

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• Author : Thomas de Grivel
  Date : 2020-05-17 12:14:58
  Hash : 955b1103
  Message : modal logic

• index.md

• # 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