On 10 Jun 2010, at 01:27, John F. Sowa wrote: (01)
> Leo, Jeff, and Elisa,
>
> I went to the TrOWL web site ( http://trowl.eu/ ) and found some
> very strange comments:
>
>> TrOWL utilises a semantic approximation to transform OWL2-DL
>> ontologies into OWL2-QL for conjunctive query answering and
>> a syntactic approximation from OWL2-DL to OWL2-EL for TBox
>> and ABox reasoning.
>
> Why does that word 'approximation' pop up twice in a single
> sentence? If you have a well-defined semantic foundation,
> all the permissible transformations are exact. (02)
In these contexts, approximation refers to a possible lossy
transformation from a more expressive representation to a less
expressive one. Hence "approximation". (03)
> Are you claiming that DL, QL, and EL have different semantics? (04)
He's definitely not. He's claiming that he can take an OWL2-DL
ontology (with NEXPTIME complex satisfiability) and rewrite it as an
OWL2-QL (with PTIME complex satisfiability) with, perhaps, some loss
of information, but that that loss of information is controlled and
suitable for various purposes. (05)
To take a simple example, I can approximate an arbitrary OWL2-DL
ontology as an RDFS ontology by extracting the asserted, explicit
subsumption hierarchy. This will be sound wrt atomic subsumptions, but
(possibly) incomplete. I can do a better approximation if I first
fully classify the ontology and then extract the subsumptions. Now, my
approximation will be sound and complete wrt atomic subsumptions in
the original ontology, but it will not be complete for arbitrary
concept expression satisfiability, subsumption, etc. nor for instance
retrieval. Plus, it requires the ontology to be classified. (06)
These are the sorts of trade off. (07)
> I can understand the idea of having different levels of
> expressive power for different subsets. But then the
> mappings between versions are just subset/superset.
>
> Why do these systems require approximations? What is the
> point of multiple notations with a common name (OWL), but
> incompatible semantics? (08)
Concept approximation is a typical non-standard service for
description logics. It can be useful for modelling as well as
performance. Unsound and incomplete approximations (more typically
incomplete) are often used as optimization inside a sound and complete
procedure (i.e., you fall back to the more complex procedure when your
sound approximation fails to return an answer). Unsound and incomplete
approximate reasoning is exposed to users when the approximations are
good enough that the user can accept the tradeoff. (09)
(This is certain by no means restricted to DLs. Anytime reasoning
procedures, if halted before completion, provide (typically) sound but
incomplete reasoning. See
http://folli.loria.fr/cds/2006/courses/Harmelen.Hitzler.Wache.ApproximateReasoningForTheSemanticWeb.pdf (010)
for more.) (011)
The most obvious common example is to use rule based implementations
of OWL Full which are known to be wildly incomplete but "useful". (012)
Cheers,
Bijan. (013)
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