|To:||"[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>, "John F. Sowa" <sowa@xxxxxxxxxxx>, Michael Gruninger <gruninger@xxxxxxxxxxxxxxx>|
|From:||Ali SH <asaegyn+out@xxxxxxxxx>|
|Date:||Tue, 20 Dec 2011 00:00:59 -0500|
I haven't been at a proper computer until today so I haven't had a chance to respond.
Thanks for the feedback.
I'm trying to identify the meat of your criticism, but as far as I can tell the discussion has focused on / taken issue with framing and emphasis.
To be clear, you're not objecting to any of the main contributions, which include, but are not limited to:
And as far as I can tell, it appears your major qualm is that we have not emphasized the link to the Lindebaum Lattice and AGM theory to your preference.
[JFS] The key generalization that cuts through the muck is something I've
Hmmm, are not partial orders a generalization of lattices?
I'd also note that back in 2006 you also wrote [http://ontolog.cim3.net/forum/uos-convene/2006-03/msg00314.html]:
On Sun, Dec 18, 2011 at 3:14 PM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
This is an excellent example of how the lattice simplifies and clarifies
To be clear, we do observe that closed hierarchies are meet-semilattices (page 8), and while we do not use the word infinimum, we do use the word meet, which is also widely used in lattice theory , [1a]. In Definition 13, we again cover the more general case of a partial order in defining the notion of Remainder. The special case where the hierarchy is a lattice is captured in Lemma 4 (page 11).
[JFS] In [my KR book], I extend the three AGM operators with a fourth operator,
With regard to the relabeling operator, we draw on work that predates this idea, and in effect define different variations of relabeling, drawing on the well developed literature re interpretations. Specifically, as we note explicitly on page 23, analogy/relabeling as you've used it, could be defined in terms of faithful interpretation (though in 2006 you seem to casually suggest is a synonym for similar to relative interpretations - http://ontolog.cim3.net/forum/uos-convene/2006-03/msg00314.html). And in my thesis, we did explicitly link the work to conceptual metaphors...
In this case, the paper's design choice was to emphasize and build on the work in  and  which was (I think) the first work to formally introduce interpreting one theory in terms of another. One reason for this design choice is that it immediately connects to the concrete and successful projects at ,  and is able to accommodate (weaker?) forms of relabeling - specifically partial, relative and faithful interpretations. In this light, analogy is the special case where the interpretation is faithful (plus a couple of other nuances, though one can't be sure based on your previous writing).
While I can appreciate you wanting a greater emphasis on the role of the AGM operators and the Lindebaum Lattice (they were indeed mentioned), the group opted to use the well established language of interpretations to formalize the various relationships in terms of hierarchies, modularity, reducibility, translations and mappings. I just quickly reviewed the definitions, lemmata and theorems in the paper, and I think only two (generously, maybe 3) might have been affected by framing the results primarily in terms of a lattice and not a partial order. Of course, in so doing, we would have also lost our more general notion of hierarchy...
The place where the AGM postulates are most relevant might be in the specification of the semantic mapping procedures. Please note that the first procedure, Finding Reducible Theories, is predicated on the general notion of interpretability, hence analogy alone would not suffice. Of course, the actual procedures themselves are quite clear on their own and draw on the various flavours of interpretation which are nowhere to be found in AGM lit.
That said, it might still be possible to provide a high level account of the procedures in terms of the AGM operators.
If one were to be charitable and extend the connection to AGM, one might consider the entire repository as undergoing a "belief" revision via the addition of novel ontologies. Following this analogy, one possible way of thinking about some of the presented procedures (especially those in section 7) is that they can be viewed as implementing a version of AGM belief revision to the entire repository. Of course, backing up this claim with actual proofs and theorems would have eaten up a few more pages and would have still required the introduction of interpretations. Similarly, I suppose one might also conceptualize a three way semantic mapping as a sort of assisted, referenced belief revision, though again, it would have required quite a few more pages to formally, precisely back up these claims. As Michael noted in off-line discussions, both these conceptualizations are extending the AGM framework to repositories as an analogy to belief revision. Perhaps we should have also highlighted the analogous connection to Schank's work on memory  and formally captured his intuition as well? :P
In contrast, in the mathematical logic of  and , the vocabulary needed to specify our intuitions are already formally specified and suffice for our purposes.
When we begin deploying reasoning services over COLORE, the AGM postulates may play a more prominent role in helping ontologists design or pick their axioms. Of course, if someone else believes that the analogy between a repository and belief revision merits a paper, they are more than welcome to write up their thoughts and back up their claims.
All in all, I appreciate that you have emphasized these connections, though we opted to use the terminology introduced in  and  and defined hierarchies via the more general partial orders. As far as I can tell, your criticism has focused not on any of our contributions or results, but style / framing and what you consider "muck" - though I submit that if you ever get around to formally capturing your intuitions at the level of detail (with all the nuances) as in this paper, you will find the "muck" to be unavoidable. In any event, I look forward to reading your upcoming Principles of Logic and Ontology textbook .
 Birkhoff, G. Lattice Theory, 3rd ed. Providence, RI: Amer. Math. Soc., 1967.
[1a] Grätzer, G. Lattice Theory: First Concepts and Distributive Lattices. San Francisco, CA: W. H. Freeman, 1971
 Burstall, R.M. and Goguen, J.A. (1977) Putting theories together to make specifications. International Joint Conference on Artificial Intelligence 1977, pp. 1045-1058.
 Enderton, H. (1972) Mathematical Introduction to Logic, Academic Press.
 Farmer,W. M. (2000) An Infrastructure for Intertheory Reasoning. Proc. of the Seventeenth Int. Conference on Automated Deduction (CADE-17), LNCS 1831, pp. 115–131.
 Schank, Roger. Tell Me A Story: A new look at real and artificial memory. Scribners, 1990.
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