Logical Sentences: => <= <=>

• Implication – (=> <sentence>* <sentence>)

  E.g., (=> (On A B) (On B C))
  
• TIV((=> ante1 … anten conse)) =
  • true when:
    • TIV(antei) is false for some I = 1, … , n; or
    • TIV (conse) is true
  • false otherwise
    E.g., (=> (On A D) (On D D))
    
  • TIV((=> a1 … an c)) = TIV ((or (not a1) … (not an) c))

• Implication – (<= <sentence> <sentence>*)

• Logical equivalence – (<=> <sentence> <sentence>)

  • TIV ((sent1 <=> sent2)) =
    • true when TIV (sent1) = TIV (sent2)
    • false otherwise
  • TIV((<=> s1 s2)) = TIV((and (=> s1 s2) (=> s2 s1)))

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