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CSC 8520 Spring 2013. Paula Matuszek

Puzzles from SYMBOLIC LOGIC By Lewis Carroll, Book VIII, Chapter 1, section 9. http://www.gutenberg.org/files/28696/28696-h/28696-h.htm. CSC 8520 Spring 2013. Paula Matuszek. (1) Babies are illogical;(2) Nobody is despised who can manage a crocodile;(3) Illogical persons are despised.

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CSC 8520 Spring 2013. Paula Matuszek

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  1. Puzzles from • SYMBOLIC LOGIC By Lewis Carroll, Book VIII, Chapter 1, section 9. • http://www.gutenberg.org/files/28696/28696-h/28696-h.htm CSC 8520 Spring 2013. Paula Matuszek

  2. (1) Babies are illogical;(2) Nobody is despised who can manage a crocodile;(3) Illogical persons are despised. • What can we conclude from these statements?1. baby(X) ⇒ ¬(logical(X)) 2. manageCroc(X) ⇒ ¬despised(X) • 3. ¬(logical(X)) ⇒ despised(X) 1a. ¬(baby(X) ∨ ¬(logical(X)) • 2a. ¬manageCroc(X) ∨ ¬despised(X) • 3a. logical(X) ∨ despised(X) • (by way of ¬( ¬(logical(X))) ∨ despised(X) ) CSC 8520 Spring 2013. Paula Matuszek

  3. Resolve 1a and 3a: • ¬baby(X) ∨ ¬logical(X) • logical(X) ∨ despised(X) • -------------------------------- • 4. ¬baby(X) ∨ despised(X) • Resolve 4 and 2a. • ¬baby(X) ∨ despised(X) • ¬manageCroc(X) ∨ ¬despised(X) • ------------------------------------- • 5. ¬baby(X) ∨ ¬manage(X) CSC 8520 Spring 2013. Paula Matuszek

  4. Turning back into implication: • 5. ¬baby(X) ∨ ¬manageCroc(X) • becomes • baby(X) ⇒ ¬manageCroc(X) • Or: babies can’t manage crocodiles! • Any other conclusions? • 1a. ¬(baby(X) ∨ ¬(logical(X)) • 2a. ¬manageCroc(X) ∨ ¬despised(X) • 3a. logical(X) ∨ despised(X) CSC 8520 Spring 2013. Paula Matuszek

  5. Any other conclusions? 1a. ¬(baby(X) ∨ ¬(logical(X)) 2a. ¬manage(X) ∨ ¬despised(X) 3a. logical(X) ∨ despised(X) CSC 8520 Spring 2013. Paula Matuszek

  6. Any other conclusions? 1a. ¬(baby(X) ∨ ¬(logical(X)) 2a. ¬manage(X) ∨ ¬despised(X) 3a. logical(X) ∨ despised(X) Resolve 2a and 3a: 6. ¬manage(X) ∨ logical(X) People who can manage crocodiles are logical. We also concluded (4) that babies are despised. CSC 8520 Spring 2013. Paula Matuszek

  7. Try these: #5.(1) No ducks waltz;(2) No officers ever decline to waltz;(3) All my poultry are ducks. CSC 8520 Spring 2013. Paula Matuszek

  8. #15. (1) All ducks in this village, that are branded ‘B,’ belong to Mrs. Bond;(2) Ducks in this village never wear lace collars, unless they are branded ‘B’;(3) Mrs. Bond has no gray ducks in this village. CSC 8520 Spring 2013. Paula Matuszek

  9. #35. (1) No birds, except ostriches, are 9 feet high; (2) There are no birds in this aviary that belong to any one but me; (3) No ostrich lives on mince-pies; (4) I have no birds less than 9 feet high. CSC 8520 Spring 2013. Paula Matuszek

  10. #44. (1) All writers, who understand human nature, are clever;(2) No one is a true poet unless he can stir the hearts of men;(3) Shakespeare wrote “Hamlet”;(4) No writer, who does not understand human nature, can stir the hearts of men;(5) None but a true poet could have written “Hamlet.”; CSC 8520 Spring 2013. Paula Matuszek

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