Re: [ontolog-forum] Intensional relation

[Juan de Nadie <juandenavas@xxxxxxxxx>]

Hi Hassan. Thanks for the answer.

This is one of the ways in that I thought. But, if we consider that "2^D" denotes the set of all subsets of D, I don't undertand what  "2^D^n" means (considering D the domain or universe, and n the arity of the relation). Which (and how much) tuples I have when I consider the set 2^D^n, let D = {a,b,c} and n=2, for example?

Thanks.

Best Regards.

2013/1/3 Hassan Aït-Kaci <hassanaitkaci@xxxxxxxxx>

On 1/2/2013 7:50 PM, Juan de Nadie wrote:

"/An intensional relation (or conceptual relation)//ρ^n of arity n on
<D,W> is a total function //ρ^n : W →_2 D^n  from the set W into the set
of all n-ary (extensional) relations on D/"

I don't understand the /_2 D^n /, mainly this base 2. Why 2? I think

that I don't understand very well the mathematical structures underlying
this notions.

Hi Juan,

The notation "2^S" for a set S denotes the set of all subsets of S - i.e., it powerset (also written P(S) sometimes). It is because its cardinality |S| is equal to 2^|S| that this notation has been used.
So if S = {a,b,c}, then 2^S = {{},{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c}}. As you can see, |S| = 3 and |2^S| = 2^|S| = 2^3 = 8.

-hak
--
http://www.hassan-ait-kaci.net/contactme.html


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