Bijan and Peter, (01)
As Peter suggested, I'm moving this discussion to Ontolog Forum. (02)
BP> ... approximation refers to a possible lossy transformation
> from a more expressive representation to a less expressive one.
> Hence "approximation". (03)
I found the word 'approximation' confusing, because it usually
means some kind of inexact matching. If you move from a less
expressive logic to a more expressive one, the mapping is exact. (04)
But if you have a more expressive logic, some statements can't
be mapped completely. Those statements may have implications,
some of which can't be mapped at all and some of which can be
mapped exactly. (05)
This also raises questions about the methodology for using
different subsets of logic. The original T-box and A-box
distinction was to use a DL to define terminology in the
T-Box, and use those terms to make FOL assertions in the
A-Box. With such a methodology, there is never a need to
go from FOL to DL. (06)
BP> TrOWL utilises a semantic approximation to transform OWL2-DL
> ontologies into OWL2-QL... (07)
Why do you use a less expressive language for queries? (08)
SQL allows full FOL in the WHERE-clause of a query, and the
evaluation can always be done in polynomial time in the worst
case -- often in logarithmic time for many queries. SQL is
not my favorite notation for logic, but people have been
happily using it for the past 30 years. (09)
Even object-oriented databases support SQL for queries against
network data, and the majority of programmers strongly prefer
SQL to the path-based notations. (010)
BP> To take a simple example, I can approximate an arbitrary
> OWL2-DL ontology as an RDFS ontology by extracting the asserted,
> explicit subsumption hierarchy. (011)
That's a reasonable thing to do. Many people use Formal Concept
Analysis (FCA) as a less expressive notation than OWL, but one
which generates the full lattice of all inheritance paths. (012)
But the word 'approximation' is misleading. It would be clearer
to call it a two-step process: (1) find a subset in the more
expressive logic, and (2) map that subset exactly. (013)
In fact, if you throw away conjunctions, you are actually
forming generalizations. Therefore, a better term would be
'generalization'. That is more accurate than 'approximation',
and it even sounds better. (014)
John Sowa (015)
-------- Original Message --------
Subject: Re: [oor-forum] FW: [Fwd: BioPortal 2.5 Released]
Date: Thu, 10 Jun 2010 09:09:50 +0100
From: Bijan Parsia <bparsia@xxxxxxxxxxxx>
Reply-To: OpenOntologyRepository-discussion <oor-forum@xxxxxxxxxxxxxxxx>
To: OpenOntologyRepository-discussion <oor-forum@xxxxxxxxxxxxxxxx> (016)
On 10 Jun 2010, at 01:27, John F. Sowa wrote: (017)
> 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. (018)
In these contexts, approximation refers to a possible lossy
transformation from a more expressive representation to a less
expressive one. Hence "approximation". (019)
> Are you claiming that DL, QL, and EL have different semantics? (020)
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. (021)
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. (022)
These are the sorts of trade off. (023)
> 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? (024)
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. (025)
(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 (026)
for more.) (027)
The most obvious common example is to use rule based implementations
of OWL Full which are known to be wildly incomplete but "useful". (028)
Cheers,
Bijan. (029)
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