Geek asks and answers

Convert sentences to first-order logic

in first order logic, I know the rules. However, when I convert some sentences to FOL, I get errors, I read a lot of books and manuals, do you have any tricks that can help me,

some examples when i make mistakes

Some children will eat any food.

C(x) means "x is a child."
F(x) means "x is food."
Eat(x,y) x eats y
I would have written like this:

(∃x)(∀y) C(x) ∧ Eat(x,y)

edit:  (∃x)(∀y) C(x) ∧  F(y) ∧ Eat(x,y)

But the book write it like this

(∃x)(C(x) ∧ (∀y)(F(y)→Eat(x,y)))

Change # 2: The 2nd type of mistake I make: Turtles rolling Rabbits.

i'm writing it like this: ∀x,y Turtle(x)  ∧  Rabbit(y)  ∧ Outlast(x,y)

 but according to the book  ∀x,y Turtle(x)  ∧  Rabbit(y)  --> Outlast(x,y)

Of course, I agree with this book, but are there any problems with my version !!

+3
source share
3 answers

WITH

∃x ∀y [C (x) ∧ F (y) ∧ Eat (x, y)]

, ∀y F (y), .. . ( " x , y, y " .) , : c ,

∀y [C (c) ∧ F (y) ∧ Eat (c, y)]

y , , c,

C (c) ∧ F (c) ∧ Eat (c, c)

.

∀x ∀y [ (x) ∧ (y) ∧ (x, y)]

,

∀x (x) ∧ ∀y Rabbit (y) ∧ ∀x ∀y Outlasts (x, y)

I.e., , , , .

→, , y, , , , , , . " Xs Ys" " X Y".

+3

, ( ) , FOL , . . :

∀ x (man(x) ⇒ ...)

- , , . , FOL . . /

Turtles outlast Rabbits.

:

  • .
  • , .
  • , .
  • .
  • ...

Btw, - APE, FOL , , , . , , FOL, , .

+2

You did not check if it was the yfirst. Given your statement, let them abe children, i.e. C(a)truly. Then (∃x)(∀y) C(x) ∧ Eat(x,y)follows (∃x) C(x) ∧ Eat(x,a). In other words, you are claiming that some children will eat anything, not just food.

+1
source

More articles:


All Articles