Re: Blank nodes, leaning, and the OWA

On Mon, Mar 28, 2011 at 12:12 AM, Pat Hayes <phayes@ihmc.us> wrote:

>  Also no *syntactic* rule that allows me to map
>
> <ex:a> <ex:p> _:x .
> _:y <ex:p> _:x .
>
> to <ex:a> <ex:p> _:x .  This looks like it should be some kind of syntactic
> reduction step, but I find nothing to justify elimination of the second
> clause except semantic considerations.
>
>
> It follows from the fact that a graph is defined to be a set of triples.
> The set {a, a} is the same as the set {a}.
>

P.S.  This is not syntax, it's semantics.  While {a,a} = {a} is true,
"{a,a}" = "{a}" is not.  By relying on the definition of set, the (implicit)
RDF abstract syntax mapping uses semantics to define a syntactic reduction.
 Compare lambda calculus; 2+3 is the same as 5, but you don't get that for
free; you have to perform a syntactic reduction by rule.  By the same token,
if you want to map

[1] <ex:foo ex:bar ex:baz>, <ex:foo, ex:bar, ex:baz>

to the abstract syntax <ex:foo ex:bar ex:baz>, you don't get to do it by
observing that a graph is a set; you have to have some explicit syntactic
rules allowing you to do it.  Otherwise it is not syntax.

-Gregg


>
>
>  The definition of instance upon which the definition of leaning depends
> only mentions "replacing some or all blank nodes"; it doesn't say which ones
> to replace
>
>
> You can replace any (or indeed none) of them, and you still have an
> instance.
>
> , it places no constraints on the replacement (except that they be bnodes,
> literals, or URI refs), and it says nothing about *removing* nodes.
>
>
> Indeed, nodes do not get removed by an instantiation.
>
>  In fact as I read it getting from a graph to an "instance which is a
> proper subgraph" is not even possible syntactically, since we have no
> syntactic rule for eliminating triples.
>
>
> A graph is a set of triples. Instantiation is defined as substituting a
> (blank node, URI or literal) for a blank node. Take the above graph and
> substitute the URI <ex:a> for the blank node  _:y. This does not affect the
> second triple, which does not contain that blank node, but it makes the
> first triple identical to the second triple. The resulting set therefore
> contains a single triple:
>
> <ex:a> <ex:p> _:x .
>
> which is a subgraph of the original graph.
>
> Make sense now?
>
> Pat
>
>
>  I suppose I'll find out such rules are right there in plain site, but I
> sure can't find them.
>
> -Gregg
>
>
> ------------------------------------------------------------
> IHMC                                     (850)434 8903 or (650)494 3973
> 40 South Alcaniz St.           (850)202 4416   office
> Pensacola                            (850)202 4440   fax
> FL 32502                              (850)291 0667   mobile
> phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes
>
>
>
>
>