quantification can be represented as an arrow from a variable to a context

http://ilrt.org/discovery/chatlogs/rdfig/2001-10-19.html#T21-13-21

SethR:  SethR wonders why quantification needs to be part of the N3 language instead of simply another labeled arc (forall or forsome) that goes from a variable to a context.

http://ilrt.org/discovery/chatlogs/rdfig/2001-10-19.html#T21-34-43

TimBl:  The difference between forAll and an arc in the normal sense? That if :x = :y in the daml:equivalentTO sense, then you can't assume from forAll x that froAll y too. 

SethR continues here ...

But why would you want to make that assumption ... maybe it's the case or maybe it's not the case.  Let's assume we are in a situation where the variables ?x ,  ?y , and ?context are URI that are also variables, and let's assume that it is the case that ?x and ?y are scoped to the same context.  This predicament is mentographed* in the animated diagram below:

http://robustai.net/mentography/quantification.html

*mentography - is just RDF graphs ... well almost ... it's kind of like labeled directed graphs meet Venn diagrams because contexts are assumed to be sets of statements and then drawn like we picture sets.

TimBl: SO they work on tokens rather than daml:equaivalnce classes.

SethR continues here ...

Huh?   By 'they' i assume you mean the URI i have called '?x'  '?y' and 'for all nodes in'  in my diagram.  SO if these are URI, then they do represent the real resources ... isn't that what you designed the URI to do?  And if they are also variables,  then they also bind to resources in some other context ... possibly the way I have depicted them doing in my diagram ... no?  What now is the problem to which you refer ?

TimBl:  Also, forSome has the problem that you can't remove a forSome triple from a formula which was true and know you have one left which is still true.

SethR continues here ...

I'm still noodeling on this one .. like the other I can't see any the problem in a way that I could graph it.  Could you give me just a little more of a hint of what the real problem is?

Seth Russell

    A graph models reality, 
    if every stated or inferred arrow in the graph 
    corresponds with a fact in reality.