3 replies to this topic

[ailearner]

i am trying to convert the english sentence below into first order logic , i i found it very hard please help

If nobody is both a child and a dog then if Fido is a dog Fido
cannot be a child

[Aereshaa]

Let D be the set of dogs.
Let C be the set of children.
(∀x (((x ∈ D) ∨ (x ∈ C)) ⇒ ((x ∈ D) ⇒ (x ∉ C)))
I dunno I'm just a tenth grader.

[Ketabat]

you can simply convert statement to First Order Logic.

∄x (Child(x) ∧ Dog(x)) but this would be equivalent to ∀x (∼Child(x) ∨ ∼Dog(x)) ,and also ∀x(Dog(x)→∼Child(x)) so:

∀x(Dog(x)→∼Child(x))
Dog(Fido)
∴∼Child(Fido)

[Nahuo]

∀x ¬(Dx ∧ Cx) → (Df → ¬Cf)
This is the way that best covers the structure of your sentences I guess
diccionary:
Dx: x is a dog
Cx: x is a child
f: fido
¬ negation
∧ conjunction
→ implication

Ofcourse given ∀x ¬(Dx ∧ Cx) you can construct a derivation to Df → ¬Cf

Edited by Nahuo, 17 January 2009 - 09:50 AM.
I was drunk last nite when I wrote it and found some miss spellings today