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Logic Exercise: Unicorn Scenarios

Explore the myth of the unicorn's traits using logical statements and resolutions in this artificial intelligence exercise from ECE457.

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Logic Exercise: Unicorn Scenarios

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  1. Exercise • If the unicorn is mythical, then it is immortal, but if it is not mythical then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. • Is the unicorn • Magical? • Horned? • Mythical? ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 1

  2. Exercise: CNF • Propositional symbols • Mythical = “The unicorn is mythical” • Immortal = “The unicorn is immortal” • Mammal = “The unicorn is a mammal” • Horned = “The unicorn is horned” • Magical = “The unicorn is magical” • If the unicorn is mythical, then it is immortal • Mythical  Immortal • ¬Mythical  Immortal ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 2

  3. Exercise: CNF • Propositional symbols • Mythical = “The unicorn is mythical” • Immortal = “The unicorn is immortal” • Mammal = “The unicorn is a mammal” • Horned = “The unicorn is horned” • Magical = “The unicorn is magical” • If it is not mythical then it is a mortal mammal • ¬Mythical  (¬Immortal  Mammal) • Mythical  (¬Immortal  Mammal) • (Mythical  ¬Immortal)  (Mythical  Mammal) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 3

  4. Exercise: CNF • Propositional symbols • Mythical = “The unicorn is mythical” • Immortal = “The unicorn is immortal” • Mammal = “The unicorn is a mammal” • Horned = “The unicorn is horned” • Magical = “The unicorn is magical” • If the unicorn is either immortal or a mammal, then it is horned • (Immortal  Mammal)  Horned • ¬(Immortal  Mammal)  Horned • (¬Immortal  ¬Mammal)  Horned • (¬Immortal  Horned)  (¬Mammal  Horned) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 4

  5. Exercise: CNF • Propositional symbols • Mythical = “The unicorn is mythical” • Immortal = “The unicorn is immortal” • Mammal = “The unicorn is a mammal” • Horned = “The unicorn is horned” • Magical = “The unicorn is magical” • The unicorn is magical if it is horned • Horned  Magical • ¬Horned  Magical ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 5

  6. Exercise: KB, Queries • KB • (¬Mythical  Immortal)  (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned)  (¬Mammal  Horned)  (¬Horned  Magical) • Negation of queries • ¬Magical • ¬Horned • ¬Mythical ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 6

  7. Exercise: Resolution, ¬Magical • (¬Mythical  Immortal)  (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned)  (¬Mammal  Horned)  (¬Horned  Magical) ¬Magical • (¬Mythical  Immortal)  (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned)  (¬Mammal  Horned)  (¬Horned  Magical) ¬Magical • (¬Mythical  Immortal)  (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned) (¬Mammal  Horned)  ¬Horned  ¬Magical • (¬Mythical  Immortal) (Mythical  ¬Immortal)  (Mythical  Mammal) ¬Immortal  ¬Mammal ¬Horned ¬Magical • ¬Mythical  (Mythical  ¬Immortal)  Mythical  ¬Immortal  ¬Mammal  ¬Horned  ¬Magical ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 7

  8. Exercise: Resolution, ¬Horned • (¬Mythical  Immortal)  (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned)  (¬Mammal  Horned)  (¬Horned  Magical) ¬Horned • (¬Mythical  Immortal)  (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned) (¬Mammal  Horned)  (¬Horned  Magical) ¬Horned • (¬Mythical  Immortal) (Mythical  ¬Immortal)  (Mythical  Mammal) ¬Immortal  ¬Mammal (¬Horned  Magical)  ¬Horned • ¬Mythical  (Mythical  ¬Immortal)  Mythical  ¬Immortal  ¬Mammal  (¬Horned  Magical)  ¬Horned ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 8

  9. Exercise: Resolution, ¬Mythical • (¬Mythical  Immortal)  (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned)  (¬Mammal  Horned)  (¬Horned  Magical) ¬Mythical • (¬Mythical  Immortal)  (Mythical  ¬Immortal) (Mythical  Mammal) (¬Immortal  Horned)  (¬Mammal  Horned)  (¬Horned  Magical) ¬Mythical • (¬Mythical  Immortal) ¬Immortal Mammal (¬Immortal  Horned)  (¬Mammal  Horned) (¬Horned  Magical) ¬Mythical • ¬Mythical  ¬Immortal  Mammal  (¬Immortal  Horned)  Horned (¬Horned  Magical)¬Mythical • ¬Mythical  ¬Immortal  Mammal  (¬Immortal  Horned)  Horned  Magical ¬Mythical ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 9

  10. Exercise: Resolution, Mythical • (¬Mythical  Immortal)  (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned)  (¬Mammal  Horned)  (¬Horned  Magical)  Mythical • (¬Mythical  Immortal) (Mythical  ¬Immortal)  (Mythical  Mammal)  (¬Immortal  Horned)  (¬Mammal  Horned)  (¬Horned  Magical) Mythical • Immortal (Mythical  ¬Immortal) (Mythical  Mammal)  (¬Immortal  Horned) (¬Mammal  Horned)  (¬Horned  Magical)  Mythical • Immortal  Mythical  (Mythical  Mammal)  Horned (¬Mammal  Horned)  (¬Horned  Magical) Mythical • Immortal  Mythical  (Mythical  Mammal)  Horned  (¬Mammal  Horned)  Magical  Mythical ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 10

  11. Exercise: Note • Previous two examples • (KB  ¬Mythical)  (Horned  Magical) • (KB  Mythical)  (Horned  Magical) • Therefore • KB  (Horned  Magical) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 11

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