Dear Ali, (01)
I've been going through the Gruninger et al. paper. It specifies more
theoretical structure than I believe is required for OOR. I cannot see
any relationship or transformation that would be useful for OOR that I
cannot define just as formally, but more simply in terms of a single
Lindenbaum lattice, the AGM operators, and a few more easy-to-define
distinctions such as conservative vs. nonconservative extensions. (02)
I would like to see a single example of a useful OOR operation that (03)
1. Could be specified in terms of that paper, but (04)
2. Could not be replaced by the same or an equally useful and
efficient OOR operation that is specified just as formally,
but much more simply in terms of the approach I outlined. (05)
> To be clear, you're not objecting to any of the main contributions,
> which include, but are not limited to:
>
> two concrete, formal definitions of modular ontology
> which are dependent on the notion of core-hierarchy,
> which in turn are dependent on recognizing the distinction
> between conservative and non-conservative extensions,
> how to arrange said modular ontologies into hierarchies that
> exhibit desirable properties
> how to define quasi-orderings over such modular hierarchies
> how to construct an ontology repository that exhibits desirable
> mathematical + computational properties
> how to implement semi-automated procedures to decompose/map
> novel ontologies into such a repository
> formal, detailed, fine-grained specifications for how theories
> in the lattice may be connected to one another
> formally defining how two ontologies are Similar and Different (06)
I don't have any quarrel with the desired functionality. But I believe
that students would find it impossible (or at least very difficult)
to learn and remember such an amorphous list of points and regurgitate
them on a final exam (or in an actual implementation). (07)
> And as far as I can tell, it appears your major qualm is that we
> have not emphasized the link to the Lindenbaum Lattice and AGM
> theory to your preference. (08)
I have no vested interest in either the Lindenbaum lattice or
the AGM operators and postulates. Following are the reasons why
I have emphasized them in my books and writings: (09)
1. Each of them requires a small number of assumptions to support
a large range of operations and applications. (010)
2. Taken together, they reduce the total number of independent
assumptions further: (011)
a) The AGM contraction and expansion operators exactly coincide
with the generalization and specialization relations of the
lattice: for every contraction/expansion that deletes/adds
a proposition to a theory, there is a corresponding
generalization/specialization and vice versa. (012)
b) The process of theory revision is *identical* to the process
of generating new ontologies by merging or modifying other
ontologies. They are nothing more nor less than two different
ways of thinking and talking about the same things -- namely
theories in a lattice. (013)
3. There is a large literature about belief (or theory) revision
that discusses the kinds of operations on ontologies in your paper.
That literature presents similar issues from a slightly different
point of view and in different terminology. They also present
many important ideas that are not discussed in your paper. See,
for example, the 110 references in the review article by Peppas. (014)
For terminology, it's important to cite all appropriate precedents
in the theoretical publications. But the list of terms to be defined
and the choice of words to talk about them should be kept to a simple,
easy to teach and learn, minimum. (015)
The subscribers to Ontolog Forum are the typical kind of people who
would need to learn and use those terms. You might write the paper
for a more sophisticated bunch of logicians. But any term needed
to explain the OOR operations must be one you would expect the
Ontolog readers to use. (016)
> are not partial orders a generalization of lattices? (017)
Every lattice is based on a partial order, but not all partial
orders determine a lattice. The entailment relation, however,
does determine a lattice. (018)
The hierarchies in your paper are *not* generalizations of lattices.
They simply select a finite subset from the infinite lattice determined
by the partial order. By not recognizing the full lattice, you get
a lot of needless complexity. (019)
> A lattice representing all possible axioms in a logic and a non-logical
> vocabulary is too coarse, as we are interested in making explicit
> and highlighting particular partial orders over selected sets of axioms. (020)
That's OK. One of the theorems about the lattices is that you can
select any particular theory as the top of some sublattice. (021)
> while we do not use the word infinimum, we do use the word meet,
> which is also widely used in lattice theory (022)
I've taught courses in which I talked about lattices, and I learned
two facts: (023)
1. Students always remember that the supremum is above and the infimum
is below. But they often confuse meets and joins. (024)
2. The word 'join' is used in many ways in computer science, and when
you apply lattices to some subjects, the different uses of the
word can cause confusion. (025)
Solution: Scratch the words 'meet' and 'join' from the approved list. (026)
> The special case where the hierarchy is a lattice is captured in
> Lemma 4 (page 11). (027)
No. The entailment relation *always* determines a lattice. The
hierarchy is just a special case of those nodes of the lattice that
happen to be represented in the current implementation. (028)
In the paper, you keep worrying about issues such as "this set
of axioms may not be itself in the hierarchy or the entire
repository." (029)
When you consider the entire lattice, every possible theory is there.
It might not be explicitly represented in the hierarchy, but you can
just create it when you need it by using the AGM operators. (030)
> 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. (031)
The word 'interpretation' is another overloaded term. You can cite
it in the publication, but every OOR operation can be defined in
terms of the lattices and the AGM operators. Delete 'interpretation'
from the approved list. (032)
> 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. (033)
I believe that the group made a mistake. I can define equivalent
notions of modularity, reducibility, translations, and mappings with
an equal level of formality. Use the term 'hierarchy' for the
implemented subsets of lattices. (034)
> the various flavours of interpretation which are nowhere to be found in AGM
>lit (035)
The AGM lit was intended for nonmonotonic reasoning. It was not
written for the problem of designing a repository. But I'm sure
that any flavors you find useful could be defined with a lot less
complexity in terms of the AGM operators. (036)
> 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. (037)
I would replace the word 'charitable' with 'sensible'. And I also claim
that the total size of your paper would be drastically reduced. The
equivalent of interpretations could be defined by walks through the
lattice -- i.e., sequences of AGM operators (plus relabeling) that
transform one theory to another. (038)
Fundamental principle: That notion of a walk through the lattice is
a very visual term. I have found it easy to explain, even to people
who have a minimal background in the theoretical issues. Those are
the kind of people who will use the OOR. (039)
> 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. (040)
I grew up as a mathematician, and all good mathematicians are lazy.
When I see that huge amount of formalism, my instant impression is that
the mathematicians who wrote it were too industrious. They started
with some badly skewed assumptions that created too much "muck",
and they just kept hacking away at the muck instead of looking
for a cleaner foundation. (041)
I apologize for being blunt. But your theory reminds me of Algol 68
-- an overly complex theory that practical programmers rejected. Even
pioneers in computer science like Dijkstra and Wirth rejected it. A
tiny amount of useful terminology survived, but most of it remains
in lame jokes about hipping, rowing, and voiding. (042)
John (043)
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