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 January 5th, 2014, 10:07 AM #1 Newbie   Joined: Jan 2014 Posts: 1 Thanks: 0 predicate logic translate the following sentences: (i) Mary has a false passport. F(m,p) (F=False, m=Mary, p=Passport) (ii) Peter likes nobody but himself. (iii) Mary only dates Americans. (iv) Smoking is dangerous. D(s) (D=dangerous, s=Smoking) (v) Not everybody cooked their own dinner. ¬?x (C(x) --> D(x,x)) (C=cooked, D=dinner) (vi) Sally wore a beautiful dress. ?x(S(x) ^ (W(x,d) ^ B(d))) (S=sally, W=wore, d=dress, B=beautiful) Unsure of the translations, any help would be great!
January 6th, 2014, 05:51 PM   #2
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Re: predicate logic

As a general remark, a translation into predicate logic depends completely on the chosen predicate symbols and constants. We could translate any sentence into just P if such symbol P is available.

Quote:
 Originally Posted by skaur (i) Mary has a false passport. F(m,p) (F=False, m=Mary, p=Passport)
I don't think having the predicate "false" apply to Mary is the most natural approach. I would suggest having a one-argument predicate F (false), a one-argument predicate P (passport; not a constant since there can be real and false passports), a two-argument predicate H(x,y) (x has y) and a constant m (Mary). Other choices of predicate symbols are possible.

Quote:
 Originally Posted by skaur (ii) Peter likes nobody but himself.
I suggest L(x,y) (x likes y) and a constant p (Peter).

Quote:
 Originally Posted by skaur (iii) Mary only dates Americans.
D(x, y) (x dates y), a unary A (American) and a constant m (Mary).

Quote:
 Originally Posted by skaur (iv) Smoking is dangerous. D(s) (D=dangerous, s=Smoking)
Seems OK.

Quote:
 Originally Posted by skaur (v) Not everybody cooked their own dinner. ¬?x (C(x) --> D(x,x)) (C=cooked, D=dinner)
I suggest B(x, y) (x belongs to y) to express "own" and C(x, y) (x cooked y).

Quote:
 Originally Posted by skaur (vi) Sally wore a beautiful dress. ?x(S(x) ^ (W(x,d) ^ B(d))) (S=sally, W=wore, d=dress, B=beautiful)
I would make Sally a constant rather than a predicate and quantify existentially over dresses.

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