Re: Revisting the abstract syntax of Named Graphs--Two alternatives

>Let's think about the abstract syntax of Named Graphs.
>
>A set of Named Graphs is a 5-tuple <N,V,U,B,L>, where
>U is a set of URIrefs;
>L is a set of literals (both plain and typed);
>B is a set of Œblankšnodes;
>U, B and L are pairwise disjoint;
>V is the union of U, B,and L.
>
>Let G be the set of all subset of the cartesian product of V,U and V.
>
>Suppose g is an element of G, let Nodes(g)={v in 
>V | there exists a t in g such that p1(t)=v or 
>p2(t)=v or p3(t)=v }.
>
>(Note: p1, p2 and p3 are projections in normal sense)
>
>It's obvious that the set of bank nodes in g, 
>written by BlankNodes(g), is the intersection of 
>B and Nodes(g).
>
>There is an equivalent relation on G,written by NameBlanked, such that
>
>g1 NameBlanked g2 iff  g1 and g2 differ only in 
>the identity of their blank nodes.
>
>Let RdfG be G/NameBlanked.
>
>Two alternatives for the definition of N:
>
>1) N is a partial function from U to RdfG.
>
>   (As Pat pointed out in a previous thread) This 
>makes it mathematically impossible for two 
>graphs to 'share' a blank node. So, no extra 
>constraint is needed to prevent blank nodes 
>being shared between different "graphs" named in 
>N.  
>
>2) N is a partial function from U to G satisfying the following constraint:
>
>    Suppose g1 = N(n1) and g2 = N(n2), if n1 != n2 then
>   
>    The intersection of BlankNodes(g1) with BlankNodes(g2) is empty.
>
>    (But it 's still possible to have that g1 
>NameBlanked g2 i.e. they are essentially the 
>same rdf graph)
>
>
>  I prefer the first one. Which one do you prefer?

For myself, I prefer to not go into this level of 
detail. I don't think its necessary: the basic 
concept of a bound variable is well known and its 
properties are well understood: there is no new 
mathematical insight to be had by re-inventing 
this wheel. Purely from a practical point of view 
there is nothing to be gained by describing 
abstract syntax at this level of mathematical 
depth. And from a purely pedagogic point of view, 
most readers of the document don't care about 
abstract syntax anyway.

All that said, I prefer the first one :-)

Pat


>
>  Any comment is welcome!
>
>
>
>Yuzhong Qu
>
>
>


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Received on Thursday, 1 July 2004 12:41:12 UTC