Re: concerns about RDF Mapping doc

Jeremy,

thanks. I now understand what you mean by non-deterministic but (bear
with me:-), can you give an example on:

[[[
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.
]]]

That would help in understanding the issue for more specific cases...

Thanks a lot

Ivan

Jeremy Carroll wrote:
> 
> 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
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 

-- 

Ivan Herman, W3C Semantic Web Activity Lead
Home: http://www.w3.org/People/Ivan/
PGP Key: http://www.ivan-herman.net/pgpkey.html
FOAF: http://www.ivan-herman.net/foaf.rdf