Interesting discussion, but please lose the attempts at humor as distracting and non-contributory.
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ali SH
Sent: Friday, October 21, 2011 7:28 AM
To: [ontolog-forum]; bparsia@xxxxxxxxxxxx
Subject: Re: [ontolog-forum] Ontologies vs Theories / Axioms vs Rules
On Fri, Oct 21, 2011 at 3:26 AM, Bijan Parsia <bparsia@xxxxxxxxxxxx> wrote:
You'll forgive me for not having interpreted your use of the term "fragment" to mean something defined in a paper which doesn't actually use the term "fragment". Since I gave concrete examples of what I meant, then I'm afraid I'm going to lay this at your feet.
It's nice and shiny, though slightly lonely lain singularly by my feet! Sorry about not anticipating this disconnect in terminology? But like you said, "who cares" what people mean when they use terms so long as someone knows their computational properties, right?
[AH] ... 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.
[BP] Yeah, that's all interesting. I've no problem with that. I'm pretty skeptical that this would enable people writing large, highly expressive ontologies in FOL, making free use of the language to decompose their ontologies into "tractable" subsets. There is, at the very least, a large engineering gap.
Except of course, we did that exactly for PSL and the Region Connection Calculus (RCC) mereotopology. And of course, given an appropriately mature repository, you could combine various mid-level modules that themselves are reducible... It's a pretty interesting engineering problem, but there's still a ways to go. Once the repository reaches a critical mass of ontology, then things get exciting.
N.B., this statement is wrong: "The major limitation of using E-connections is that the use of such modules as a means
of reﬁning an ontology (non-conservative extensions of a theory) becomes impossible."
Nothing prevents you from non-conservatively extending within a e-connection based module, or from altering the module structure. A decomposition based approach does exactly that. A syntactic enforcement approach would be otherwise, but even there, within module is fine and all breaking modular structure means is that you go through some extra syntactic hoops.
If you say so... I defer to Oliver K here.
[AH] 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.
[BP] The phrase "at least first order expressivity" needs clarification. My usually understanding is something like, "Does not fall into any known decidable fragment of FOL."
Not really sure how to respond to this. There are two cases illustrated above. One, where an ontology comprises of a union of multiple modules with at least one module requiring expressivity. A system trying to reason over a query that uses language from all the modules would require that full expressivity (even if it ends up not really exploiting it). Being able to do such decomposition further allows one to optimize for those queries not requiring the full breadth of the ontology.
Two you have some ontology written in FOL (i.e. PSL). You show that models of PSL-core is reducible to simpler structures. This suggests one way to optimize implementation of such system that generate PSL compliant models. Something about not trying to optimize prematurely.
But you're right, there are two parallel issues here. One is the actual reasoning involved, and the other re syntactic limitations imposed by a particular representation language. As John Sowa likes to point out, it is perfectly possible to write programs that never halt in any interesting programming language. However, people don't syntactically restrict programming languages in order to ensure the worst case cannot possibly be encountered. In this vein, the same applies to FOL. Except of course, ontology engineering is still in relative infancy compared to traditional programming, and it's easy to write "infinite loops."
But the issue is one of not getting caught up in syntactic limitations, and focusing on capturing the intuition clearly and faithfully. Or rather, emphasizing/focusing on the actual domain and the content of ontologies rather than trying to prematurely optimize based on syntax. (sorry, couldn't resist)
[AH] Right, so the problem of tractability is part of the domain moreso than an inherent part of a representation language.
[BP] Well, this calls into doubt your earlier claim to knowledge. This does not REMOTELY follow, at least on any reasonable interpretation I can find.
Apologies, poor phrasing. It was a rather obtuse way of repeating (what others have said multiply), that it doesn't matter what language you use, but that complexity, intractability, exponential time, etc are very much due to the nature of certain problems. Syntactic limitations don't change the problem domain, they just don't let you express / represent it.
[BP] Ok. I don't care at all about OOR.
[AH] Funny that you're on the OOR mailing list then :P.
Lol, seriously? I was just poking fun. I do appreciate your contributions, you've stimulated some thought and I appreciated your pointers to recent research in DL reasoning.
Ah sure, you mean standard notions such as conservative extension. Well, CE for sure will be nasty (undecidable) for OWL alone, so detecting such relations is probably unlikely in the near future. If you have an approximation algorithm, however, you might be able to put some guarantees on the output. And in the OWL world we've worked on various approximations of CE related notions (cf locality based modules).
Though in contrast with most DL research, we've focused more on flavours of non-conservative extensions.
I don't think the problem of deciding whether a theory is not a conservative extension of another is any easier than one that is.
Good thing that's not what we're claiming! :D
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