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Re: concerns about RDF Mapping doc

From: Jeremy Carroll <jjc@hpl.hp.com>
Date: Fri, 19 Oct 2007 16:21:49 +0100
Message-ID: <4718CB8D.5080803@hpl.hp.com>
To: Ivan Herman <ivan@w3.org>
CC: public-owl-wg@w3.org

Ivan Herman wrote:
> Jeremy,
> 
> I am not ashamed to acknowledge my own missing technical knowledge...:-)
> could you explain (or give specific references) to your points (b) and
> (c) below?
> 

I've been struggling to articulate point (b) to myself today, this is 
where I've got to. I'll try and articulate better on Monday, and also 
address (c) next week.

I am having to think quite hard to justify the concern - so this is a 
first attempt.

In this first attempt I will pretend that the resolution of webont issue 
5.3 was iff rather than the actual if-then.
http://www.w3.org/2001/sw/WebOnt/webont-issues.html#I5.3-Semantic-Layering

I will use iff* for a pretend iff, that refers back to this point, etc.

(More on this point next week I guess).



> Thanks
> 
> Ivan
> 
> Jeremy Carroll wrote:
>>
>> b) In OWL 1.0, the tension between the OWL Full semantics and the direct
>> semantics is resolved in cleverly non-deterministic mapping rules
>>

The OWL DL vs OWL Full issue in v 1.0 is resolved in the following way:

There is an OWL DL syntax and semantics: abstract syntax trees (AST) and 
the direct semantics.

There is an OWL Full syntax and semantics: graphs and the RDFS 
compatible semantics.

For each of these, we can form equivalence classes of ontologies that 
have the same meaning:

i.e.

ASTs t1 and t2 are equivalent if t1 entails t2 and t2 entails t1 under 
the direct semantics

Graphs g1 and g2 are equivalent if g1 entails g2 and g2 entails g1 under 
the RDFS compatible semantics.

The mapping rules relate ASTs with Graphs in a way that aligns the 
semantics. So if
t1 m g1
and
t3 m g3
then
t1 direct-entails t3 iff* g1 full-entails g3

Overall we get a relationship between the equivalence relationships over 
ASTs and over graphs, via the mapping rules.

i.e. If

g1 m t1

g2 m t2

then

{

t1 ~ t2

iff

g1 ~ g2

}

[I still need to think through the iff* issue here]

Thus any subset of an equivalence class of trees is mapped to a subset 
of equivelance class of graphs, and conversely.

Some of the equivalent ASTs will be equivalent becasue of syntactic 
variation in trees that does not correspond to a syntactic variation of 
graphs.

Some of the equivalent graphs will be equivalent becasue of syntactic 
variation in graphs that does not correspond to a syntactic variation of 
trees.

Some of the equivalent graphs will have corresponding equivalent trees 
in which the syntactic variations are similar.

If the mapping rules are too strict then each graph and each tree will 
map to only a small number (e.g. 0, 1 or 2) of trees or graphs.
If the mapping rules are looser (non-deterministic) then much of the 
equivalence relationships are built into the mapping rules.


With strict (deterministic) rules, the following are likely:
a) large numbers of graphs which have no equivalent trees
b) no easy to articulate rationale for which graphs have trees and which 
don't
c) unnecessary algorithmic complexity in determining whether a 
particular graph does or does not have a tree representation


All three of these issues arose in OWL 1.0 development, and in my 
opinion, they all are derivative from the overall problem framework, and 
are symptons of trying to align the trees and graphs in too fine grain a 
fashion. The non-determinism that was gradually introduced during the 
OWL 1.0 development, while being horrible from some point of view, fixed 
the underlying granularity problem, because the non-determistic rules 
are about aligning equivalence classes of trees with equivalence classes 
of graphs, rather than individual trees with individual graphs.

Hmmmm - that's where I've got to today, but it doesn't feel like what I 
wanted to say at all! I've moved from semantic articulation to the 
syntactic ....

I'll try again Monday.

Jeremy
Received on Friday, 19 October 2007 15:22:23 GMT

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