Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How can i create a sentence in FOL which contains a quantum of subjects? E.g. "Five students took Greek in spring 2001."

I can phrase something like "One student took Greek in spring 2001" with:

∀xy : (took(x, Greek, Spring2001) ∧ took(y, Greek, Spring2001)) ⇒ (x = y)

For sure i can chain this phrase until all subjects (x, y, z, ...) are defined, but are there any patterns to do this?

share|improve this question
add comment

migrated from stackoverflow.com Nov 27 '12 at 15:36

This question came from our site for professional and enthusiast programmers.

1 Answer

up vote 1 down vote accepted

Assert the existence of five objects, say $\exists x_1, \cdots \exists x_5$, then state that they are all unequal, so $(x_1 \neq x_2),(x_2 \neq x_3),(x_1 \neq x_3), \cdots $ (there will be $5 \choose 2$ such expressions), then state that they each took Greek, and then state that if $z$ took Greek, then $z=x_1$ or $z=x_2$ ... or $z=x_5$ (presuming that exactly five students took Greek).

share|improve this answer
    
Thanks for that. I hoped that they exists other methods to prevent defining 2^5 expressions. Anyway, thanks ;) –  Slevin Dec 3 '12 at 16:07
    
$32 = 2^5 \neq {5 \choose 2} = 10$, but I see your point. –  Isaac Solomon Dec 3 '12 at 18:38
    
Sorry, misspelled. –  Slevin Dec 4 '12 at 9:36
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.