|From:||Ali SH <asaegyn+out@xxxxxxxxx>|
|Date:||Thu, 20 Oct 2011 21:57:05 -0400|
On Thu, Oct 20, 2011 at 4:08 PM, Bijan Parsia <bparsia@xxxxxxxxxxxx> wrote:
Hmmmm, sorry, not so quite. ;)
I think though that we're talking at cross purposes. By fragment, I meant that which is given by definition 13 in http://stl.mie.utoronto.ca/publications/colore-fois.pdf
Namely (though see the paper for proper formatting and symbols):
which leads to the theorem:
... Basically, see section 3.4 in that paper for a proper treatment of what I meant by fragment. It is in this sense that T* is a fragment of T.
Sure, imagine an ontology that is a union of modules for a subclass taxonomy, time and geo-spatial components. The theory that combined all these modules requires at least first order expressivity to capture intuitions about the domain. It is tractable, but answers take on the order 3-20 minutes to return based on a kb and a general purpose FOL reasoner. However, properties of each of the modules are also known, and they each have a dedicated reasoners just in case the system receives a query involving vocabulary singularly to do with one of the sub-modules. For example, if a query involves language only drawn from the taxonomic sub-module, then the FOL reasoner need not be called, and instead something optimized for traversing trees might be invoked. Alternatively, if a query involved solely geospatial terms, then perhaps no reasoner would actually be called, but the query would be computed algebraically.
It is my (perhaps faulty) understanding that the Cyc system does something broadly similar to this.
For another example, consider the PSL-core ontology which is reducible to simpler theories, and these more simple models can be used to construct models of the PSL-core ontology (section 3.5 of the paper referenced above).
Thanks, I know this, and I haven't been talking about size...
Right, so the problem of tractability is part of the domain moreso than an inherent part of a representation language. FOL for all its semi-decidability might still be quite tractable and fast, and OWL for all its decidability might take a super long time... It's more to do with what you're modelling than your language.B ut this is beside the point here. The rest of your response continues to assume that I'm simply talking about "size" which is certainly not the case.
Funny that you're on the OOR mailing list then :P.
Though in contrast with most DL research, we've focused more on flavours of non-conservative extensions. I'll see if there is a pre-print version of an upcoming Applied Ontology paper, though there's a very preliminary sketch of such a procedure for generating reducibility between (i.e. factoring) ontologies in Chapter 5 of https://tspace.library.utoronto.ca/bitstream/1807/17512/1/Hashemi_Ali_200906_MASc_thesis.pdf. I should reiterate that it has been *significantly* updated in the more recent paper, and I will link the pre-print once it is available.
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