Re: union of graphs [soolved with a minor issue]

On Jun 25, 2013, at 10:58 AM, Antoine Zimmermann wrote:

> As a previous email of mine indicated, we can consider my objection to the definition of entailments with sets moot and move on.
> 
> The simple solution that Peter proposed is indeed very good.

Yes, it was an excellent idea. 

> There subsists residue of the previous design:

The actual *design* has not changed. 

> 
> """
> In order to capture the full meaning of graphs sharing a blank node, it is necessary to consider the union graph containing all the triples which contain the blank node.
> """
> 
> This suggests that union is the only logical operation that makes sense.

Not at all. 

> People *can* consider the merge instead.

Yes, quite. The merge is always a valid consequent ot any set of graphs. But it may lose information. The most obvious way to illustrate this is to take any graph with blank nodes and divide it into its separate triples, considering each one to be a separate graph. The merge of this set of graphs will be completely disconnected, with no two triples sharing a blank node. 

> 
> With union, there are strange properties of RDF graphs:
> 
> if X is equivalent to Y, it would seem logical that {X, Y} is equivalent to X (X being equivalent to Y seems to intuitively mean that Y does not bring any information in addition to X, so the set {X, Y} should be equivalent to Y. But this is not the case if you definition the truth of {X, Y} as the union of X and Y.
> 
> E.g., if b1 and b2 are two different blank nodes, then:
> 
> (b1, <p>, b2)  is equivalent to  (b2, <p>, b1).

Considered in isolation, that is true, because each triple expresses only part of what follows from those two graphs taken together. Graphs which share blank nodes mean more, taken together, than can be determined by considering their truth conditions in isolation. 

> Clearly, there is no gain of information when you know one or the other.
> Yet, the union says something more.

Yes. The two graphs together assert that: (1) there are two things A, B such that p(A, B) and p(B, A). The two triples in isolation assert respectively that (2) there are two things A, B such that p(A,B) and (3) there are two things A, B such that p(B,A). (2) and (3) are equivalent, but (1) is more information than the conjunction of (2) and (3).

> This also means that one should never copy a graph using different bnodes, because they really lose information.

If a single blank node occurs in several triples, and you replace this blank node in some of those triples but not in others, by a different blank node, then indeed, you lose some information. This applies whether these triples are in a single graph or in multiple graphs. The result is still entailed, of course, so this is not an invalid or incorrect operation, but it does lose some information. 

In general, if you mess with blank nodes, then you should make sure you have *all* the triples that contain that blank node. 

> If I copy the first graph above, using bnodes b3, b4 instead of b1 and b2, leading to (b3, <p>, b4), then I can't compute the inferences that I would have had with the original graphs. Yet, I only made truth-preserving operations. How can this be?

Because (to repeat) the full content of graphs with shared blank nodes is not fully captured by their truth-conditions in isolation. Just as the full meaning of the conjunction 

P(x) & Q(x)

is not captured by the truth conditions on the two atomic sentences P(x) and Q(x) treated separately, when free variables are understood existentially. Because that separate treatment fails to take into account that fact that a variable (or blank node) is *shared*. 

> To summarise, it is possible to apply a sequence of presumably "truth-preserving" operations and end up doing something that is not truth-preserving.

Creating a graph by assembling a set of triples is not truth-preserving, if you treat each triple as a separate graph. So should RDF graphs be illegal?

Pat


> This is simply because union of graphs is not truth-preserving.
> -- 
> Antoine Zimmermann
> ISCOD / LSTI - Institut Henri Fayol
> École Nationale Supérieure des Mines de Saint-Étienne
> 158 cours Fauriel
> 42023 Saint-Étienne Cedex 2
> France
> Tél:+33(0)4 77 42 66 03
> Fax:+33(0)4 77 42 66 66
> http://zimmer.aprilfoolsreview.com/
> 

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Received on Wednesday, 26 June 2013 03:00:46 UTC