> 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.