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First-Order Logic

  1. May 31, 2004 #1
    Represent this sentence in first-order logic:
    Every student who takes French passes it.

    Represent the sentence "All Germans speak the same languages" in predicate calculus. Use Speaks(x, l), meaning that person x speaks language l.

    What axiom is needed to infer the fact Female(Laura) given the facts Male(Jim) and Spouse(Jim, Laura)?
     
  2. jcsd
  3. May 31, 2004 #2

    AKG

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    Hopefully, you can figure out the actual syntax yourself (I can't) but it might be helpful to see the first sentence as:

    For all students, s, (s takes French) --> (s passes French)

    For the third one, the axiom would be that only a male and a female can be spouses. Maybe:

    For all x, y, (Spouse(x,y)) --> (male(x) <--> female(y))

    Maybe also

    For all x, male(x) <--> ~female(x)
    OR
    For all x, male(x) <--> !female(x)
    depending on what notation you're using.
     
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