Translation into FOL Sentences

Let S(x) mean x is a skier, M(x) mean x is a mountain climber, and L(x,y) mean x likes y, where the domain of the first variable is Hoofers Club members, and the domain of the second variable is snow and rain. We can now translate the above English sentences into the following FOL wffs:

  1. (∀x) S(x) ∨ M(x)
  2. ¬(∃x) M(x) ∧ L(x, Rain)
  3. (∀x) S(x) ⇒ L(x, Snow)
  4. (∀y) L(Ellen, y) ⇔ ¬L(Tony, y)
  5. L(Tony, Rain)
  6. L(Tony, Snow)

  7. Query: (∃x) M(x) ∧ ¬S(x)
  8. Negation of the Query: ¬(∃x) M(x) ∧ ¬S(x)

  • Conversion to Clause Form

    1. S(x1) ∨ M(x1)
    2. ¬M(x2) ∨ ¬L(x2, Rain)
    3. ¬S(x3) ∨ L(x3, Snow)
    4. ¬L(Tony, x4) ∨ ¬L(Ellen, x4)
    5. L(Tony, x5) ∨ L(Ellen, x5)
    6. L(Tony, Rain)
    7. L(Tony, Snow)
    8. Negation of the Query: ¬M(x7) ∨ S(x7)