Re: [ontolog-forum] Ontology, Analogies and Mapping Disparate Fields

[Ali SH <asaegyn+out@xxxxxxxxx>]

A download link is available here: http://dl.dropbox.com/u/856524/gruninger-etal-modfol-2011.pdf

Modular First-Order Ontologies via Repositories
Michael GRÜNINGER, Torsten HAHMANN, Ali HASHEMI, Darren ONG, Atalay OZGOVDE

Abstract. From its inception, the focus of ontological engineering has been to support the reusability and shareability of ontologies, as well as interoperability of ontology based software systems. Among the approaches employed to address these challenges have been ontology repositories and the modularization of ontologies. In this paper we combine these approaches and use the relationships between first-order ontologies within a repository (such as non-conservative extension and relative interpretation) to characterize the criteria for modularity. In particular, we introduce the notion of core hierarchies, which are sets of theories with the same non-logical lexicons and which are all non-conservative extensions of a unique root theory. The technique of relative interpretation leads to the notion of reducibility of a theory to a set of theories in different core hierarchies. We show how these relationships support a semi-automated procedure that decomposes an ontology into irreducible modules. We also propose a semi-automated procedure that can use the relationships between modules to characterize which modules can be shared and reused among different ontologies.

On Wed, Dec 14, 2011 at 10:32 AM, Michael Gruninger <mudcat@xxxxxxxxxxxxxxx> wrote:

Hi Ali,
here is the submitted version of the modularity paper.
You can put it up on your own url somewhere until it is
accepted by Applied Ontology.

- michael

Quoting Ali SH <asaegyn+out@xxxxxxxxx>:

> Hi all,
>
> Just wanted to pass along a link to an ontology related story (though it's
> barely framed as such) in a relatively mainstream technology news outlet:
> http://www.physorg.com/news/2011-12-link-patterns-spider-silk-melodies.html
>
> While these are the originating papers (
> http://arxiv.org/ftp/arxiv/papers/1111/1111.5297.pdf [1]) and (
> http://math.mit.edu/~dspivak/informatics/ologs--basic.pdf [2])
>
> It seems to me that the author is reinventing the wheel (though with a nice
> twist re formulating / expressing o-logs and "sketches").
>

> Especially since their review of the ontology field (in the *
> ologs--basic.pdf* paper) seems to extend only to RDF/OWL and completely

> ignores (or misses) work on Common Logic, conceptual graphs and the most
> glaring omission - the work on category theory in Bremen. Incidentally,
> such an omission appears to be an unfortunate corollary of the crowding out
> of any non-RDF/OWL work.
>
> In any event, it's interesting work, though the correlation between the two
> seemingly disparate fields (spider silks and melody) reminds me more of the
> seminal "Unreasonable Effectiveness of Mathematics in the Natural Sciences"
> speech - http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html [3]
>
> A lot of semantic mapping to date has indeed focused on DL level mappings
> (cf Euzenat & Shvaiko's Ontology Matching book [4]), but there is a rich
> set of logical mappings which can capture a lot of these structural
> similarities between disparate fields. I know I've repeated this claim
> before, but the limited expressivity of DL's mutes many of these mappings,
> because well, they generally aren't captured (can't be expressed) in the
> formalism. There is something to be said for picking the correct language
> to describe a domain, where difficult problems become much simpler. I
> suspect this will be one of the first major obstacles in orchestrating
> services based on LOD sets beyond the low hanging fruit currently being
> explored.
>
> In a previous discussion with Bijan, we were talking past each other re
> reasoning over expressive ontologies. I kept on talking about reasoning
> "off-line", while he insisted such projects were fatally intractable. I
> later realized the disconnect was that I was talking about verifying an
> expressive ontology (which you only need to do once, hence off-line), while
> he was thinking that you need to process the entire ontology for every
> query. Verification need be done only once (and indeed, off-line), while
> the deployment of queries over fragments of the ontology can then deploy
> more optimized tools.
>
> I think there's an attractive case for articulating in some way, in some
> place, an expressive version of an ontology, even if for certain services /
> tasks you only deploy a decidable fragment of said ontology. For one, it
> can greatly facilitate semantic mappings, while secondly, it makes the
> entire project more upwards compatible, especially as the major DL's are
> continually adding greater expressivity. The expressive version of the
> reference ontology can function a sort of road map for deployment, a sort
> of technology agnostic commitment, whereas DL or otherwise deployed
> artifacts are technology dependent products / services...
>
> Lastly, I'd point out that the group at the University of Toronto does have
> a paper on this topic (modularizing and reducing expressive ontologies into
> ontologies of other types that preserve the logical structure of the
> models), which has the incidental benefit of being able to identify logical
> similarity between theories according to an open repository... I will see
> if I have permission to distribute a pre-print to the list (Michael?).
>
> ===
> [1] Tristan Giesa, David I. Spivak and Markus J. Buehler "Reoccurring
> Patterns in Hierarchical Protein Materials and Music: The Power of
> Analogies" BioNanoScience Volume 1, Number 4, 153–161, DOI:
> 10.1007/s12668-011-0022-5
> [2] D.I. Spivak, R.E. Kent “Ologs: a categorical framework for knowledge
> representation". PLoS ONE (in press): e24274. (2011)
> doi:10.1371/journal.pone.0024274
> [3] Wigner, E. P. (1960). "The unreasonable effectiveness of mathematics in
> the natural sciences. Richard courant lecture in mathematical sciences
> delivered at New York University, May 11, 1959". Communications on Pure and
> Applied Mathematics 13: 1–14. doi:10.1002/cpa.3160130102.

> [4] Jérôme Euzenat, Pavel Shvaiko. *Ontology Matching*. Springer-Verlag,

> Berlin Heidelberg (DE), 2007
>
> Best,
> Ali
>

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