Re: Blank nodes, leaning, and the OWA

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

>
> On Mar 27, 2011, at 10:16 PM, Gregg Reynolds wrote:
>
> On Sun, Mar 27, 2011 at 10:16 AM, Pat Hayes <phayes@ihmc.us> wrote:
>
>>
>> On Mar 27, 2011, at 12:13 AM, Gregg Reynolds wrote:
>>
> ...
>
>> [1] a)  <ex:Pedro ex:owns _:x>, <_:x rdf:type ex:Donkey>, <_:x ex:name
>> ex:Daisy>
>>      b)  <ex:Pedro ex:owns _:y>, <_:y rdf:type ex:Donkey>, <_:y ex:name
>> ex:Maisy>
>>
>> ...
>
>> Is the graph of [1] lean?  It seems to me that under the OWA the answer
>> must be that we do not know,
>>
>>
>> It is lean, and we do know this. Leanness is a syntactic property of the
>> graph. You can determine it algorithmically.
>>
> ...
>
>> You apparently do not understand it. Check out the definitions in the
>> specs, they are given quite unambiguously. A graph is lean when it is has no
>> instance which is a proper subgraph of itself. The graph [1] does not have
>> such an instance, so it is lean. Nothing to do with models!
>>
>> Trust me, I've spent more hours than I care to count trying to decipher
> the specs.  Whatever they are intended to convey may be unambiguous; what
> the text actually says is another matter.  For example, I find no syntactic
> rules that allow me to map a piece of concrete syntax to the abstract
> syntax.
>
>
> See http://www.w3.org/TR/2004/REC-rdf-testcases-20040210/#ntriples and the
> table given there.
>

The table that maps N-Triple productions to RDF *Concepts*, and nodeID to
"Identifier for a blank node"?  Concepts are not syntax, and blank nodes in
RDF graphs do not have identifiers.

> Nothing that says explicitly that e.g. every _:x should map to one blank
> node, nor that distinct bnode IDs cannot map to one bnode.
>
>
> Is that not utterly obvious? Why else would one call it an "identifier for
> a blank node" ?
>

I wish it were as obvious as it looks.  But since the specs are inconsistent
in their use of "blank node" and "blank node identifier" (among other
things), what looks "obvious" is not to be trusted.

>  For that matter, nothing that says the mapping must preserve URIs.
>
>
> The URIs used in the n-triples notation (used throughout the semantics
> document) are *identical* to the URIs in the abstract syntax. I fail to see
> how they can fail to be 'preserved' under these circumstances.
>

See note on "obvious" above.

>
>  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}.
>

Ok.  It's not what I think of when I see the term "abstract syntax", but I
grant that it works (modulo instantiation, see below).

>
>  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.
>

By the definition of instantiation, it is also legal to replace _:y by *any*
URI.  In particular, it is legal to use <ex:a> to replace _:x in

<ex:a> <ex:p> _:x .
_:x <ex:p> _:x .

yielding <ex:a ex:p ex:a> .  It may not be a proper subgraph of the original
graph, but it is a legal mapping of it.  Maybe a definition of graph
normalization would be useful.

>
> Make sense now?
>
> Yes, I see the ideas behind the prose, and thank you for taking the time.
 Do you see the ambiguities?

Strictly speaking, RDF Abstract Syntax is not syntax, since it has no symbol
for blank nodes.  No syntax without symbols.  But even if we overlook
that, RDF's notion of "abstract syntax" is unorthodox.    At least some of
your readers (and when I say some, I mean at least one, i.e. me) will think
of concrete v. abstract syntax in terms of parse trees and abstract syntax
trees (cf Aho Seti and Ullman's Dragon book), which is not how RDF uses the
terms.  RDF abstract syntax looks much more like semantics to me.  Do you
see why I say that?  Again, this is a question of how the text works, not
the ideas motivating the text.  Every reader comes to the text with ideas
about what certain terms mean; usage that deviates from "standard" (or at
least widespread) usage should be explicitly motivated.

Thanks,

Gregg