Relational Image

maths~reader

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Oct 26, 2011
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Hi all,

I have simple question, i would like to just make sure if this is valid thing in generating set equation bellow

Is

\(\displaystyle {\ p:person\bullet\mid\ p \mapsto #(ParentOf ; ParentOf)\ (\ p\ )\ }\)

same as

\(\displaystyle {\ p:person\bullet\mid\ p \mapsto #(ParentOf\ (\ ParentOf\ (\ p\ )\ )\ )\ }\)

??

Please note: '(' ')' represent relational image ( half open and half close bracket) from the set relation concept. I couldn't find a latex command for it.

Thanks
 
\(\displaystyle {\ p:person\bullet\mid\ p \mapsto #(ParentOf ; ParentOf)\ (\ p\ )\ }\)
same as
\(\displaystyle {\ p:person\bullet\mid\ p \mapsto #(ParentOf\ (\ ParentOf\ (\ p\ )\ )\ )\ }\)
It is very hard to follow that notation.
However, \(\displaystyle p\mapsto P\circ P(p)\) is the same as \(\displaystyle p\mapsto P[P(p)]\)
That is far from standard notation in formal logic.
 
Thank very much pka for the replly. I'm sorry i should i should have put more information. ParentOf is relation with source being elements of Person (parent) mapping onto target with set of childern.

So the above relation is basically calculating the no the grandchildren has for a given person, p.

I'm not sure what the [] means there?

Thanks
 
Thank very much pka for the replly. I'm sorry i should i should have put more information. ParentOf is relation with source being elements of Person (parent) mapping onto target with set of childern.
So the above relation is basically calculating the no the grandchildren has for a given person, p.
I'm not sure what the [] means there?
[] are just grouping symbols.
\(\displaystyle P\circ P(p)=P(P(p))\) would read "the parent of the parent of p".
 
ahh in that case, my both alternative set comperhension was right!
Actually there is a move on to have
\(\displaystyle P_{[n]} (x) = \underbrace {P \circ P \circ \cdots \circ P(x)}_{\text{n times}}\)
 
I actually see problem with my alternative now. Don’t think my alternative could have been right. My original expression with the compound relation actually explicitly tells that given a p of Person i could derive set of children. Because it shows as follow

\(\displaystyle \underbrace{Person \rightarrow Person}_{\text{ParentOf}}\ \semicolon \underbrace{Person \rightarrow Person}_{\text{ParentOf}} \)

With that ParentOf ; ParentOf would clearly tells that its a compound relation for with given p a set of children can be retrived using the relation parentOf.

But when I do this ParentOf( ParentOf( p ) ). There is no explicit relation showing of compound. Doing this could produce an ambiguity that ParentOf could be refereeing to the same relation twice.

Thanks
 
I actually see problem with my alternative now. Don’t think my alternative could have been right. My original expression with the compound relation actually explicitly tells that given a p of Person i could derive set of children. Because it shows as follow
\(\displaystyle \underbrace{Person \rightarrow Person}_{\text{ParentOf}}\ \semicolon \underbrace{Person \rightarrow Person}_{\text{ParentOf}} \)

With that ParentOf ; ParentOf would clearly tells that its a compound relation for with given p a set of children can be retrived using the relation parentOf.

But when I do this ParentOf( ParentOf( p ) ). There is no explicit relation showing of compound. Doing this could produce an ambiguity that ParentOf could be refereeing to the same relation twice
Actually, it seems to me, you are trying to impose you own notation onto a very well established field. Let us suppose that \(\displaystyle P~\&~Q\) are each

\(\displaystyle (x,y) \in P \circ Q\)
\(\displaystyle \left( {\exists t} \right)\left[ {(x,t) \in Q \wedge (t,y) \in P} \right]
\)

You seems to me that you dislike standard logical notation. WHY?
 
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