[ontolog-forum] Using Repositories for Ontology Design and Semantic Mapp

[Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>]

Hello all,

Last week in the Next Steps in Using Ontologies as
Standards discussion, I alluded to some of the work I did for my thesis
and how it related to the topic at hand.

Well, I've finally bound and submitted it, so I'm going to share it with all of you.

The thesis has three main contributions which i think are of immediate interest to the ontology community:

• an architecture for ontology repositories

that enable

• an ontology design algorithm (with correctness proof)
  
• a semantic mapping algorithm (with correctness proof)

A quick overview:

Thus it uses (1) ontology repositories as a centralized, semi-open, inverted pseudo-upper level ontology to facilitate (2) ontology design and (3) semantic mapping.


The Repository

It's semi open in that
any one can submit theories for inclusion (though there is a vetting
process). I will explain the pseudo-UO below.

It is predicated on the idea of metaphor - that disparate concepts share underlying logical substructures.

The repository is organized in two directions: it consists of
"abstraction layers" and within those abstraction layers, it contains
"core-hierarchies." It uses a loose notion of primitive, which i call
logical lego blocks. These theories populate the lowest layer of the
repository, and are connected to other layers by either Representation
Theorems or Mapping Axioms (we're unsure which is the best way to move
forward). The two following algorithms do not rely on how the layers are connected to one another.

The theories of the lowest level are drawn from mathematics, and include
but are not limited to symmetries, orderings, groups, geometries,
topologies etc.
The layer atop is more akin to traditional Upper Ontologies (UO), and
is populated by concepts such as space, time, mereotopologies, etc.
Additional layers may be added, corresponding to more specialized
theories.

A key difference with a UO is that we're not taking a position on what is the
correct concept of space, time etc. Instead, it relies on what the
language can express (i call it, its biases). Thus the lowest layer is
fundamentally about how the rules of FOL let us define interesting
theories just by looking at abstract symbols. The other layers which
connect to the real world, then come on top.

A core-hierarchy consists of non-conservative extensions of one
theory (or relation). I've implemented one for partial orders. So at
the root of the hierarchy are the basic poset axioms, and further
modules (theories) that extend that theory, in effect construct a map
of poset theories. The only stipulation is that no core-hierarchy can
share a
non-conservative extension with another core-hierarchy in the same
abstraction layer.

Ontology Design Algorithm

With this stipulation, I can construct an ontology design algorithm.

The
novelty
of the approach is two-fold. First, it does not require a
subject matter expert to be well versed in FOL (or CL), either
theoretically or with its syntax / grammar. Second, it relies on a
model theoretic approach to axiom specification. Thus, instead of
writing axioms, users define
relations based on their models (in the Tarski sense). Basically, I ask
a user to construct at least one model for the relation they
are trying
to define. They do so in a Sandbox Environment which i have thus far
implemented for binary relations, in the guise of a graph. A complete
diagram (set of all positive and negative literals), is then generated
from each user model. The only stipulation for how models can be drawn
is that the same complete diagram may be generated unambiguously and
repeatedly for a given "picture".

These FOL statements (the complete diargam) are now tested against
an abstract layer with each (or user specified) core-hierarchy.
Basically, we will scour the repository and see
which theories are satisfied by this model.

However, clearly
this is not enough to get at the user's intended axioms. Once we have
identified the theories in the repository that are consistent with the
user models, we look to the scientific method (falsification) and the map we have of
each hierarchy to intelligently traverse the repository to find "the strongest set
of axioms which capture the user's intended models."

We do so by generating models and proposing them to the user. In
this way, we grow sets of Accepted and Rejected models. Based on user
feedback, we arrive at the strongest theories in the repository that
capture the user's intended models. All without requiring the user to
know FOL particularly well, or even look at the underlying axioms. They
only need to be able to "draw" one model of their idea, and to
determine whether a proposed model fits their view or not. The nuances
of this approach (as well as a correctness proof) are available in the
thesis. I'd like to stress that this approach need not be restricted to
simply visual models. Conceivably, it can be extended to auditory,
tactile and other senses. Again the only stipulation is that the model
may be unambiguously and repeatedly interpreted in the same way.

Semantic Mapping Algorithm

Similarly,
given a repository with the above architecture, we can conduct
semi-automatic semantic mappings. The mapping being done is that of
alignment as specified by Choi and Noy (see thesis for references and
more detail).

We can create alignment between n ontologies. The way it
works is simple. The axioms for a single target ontology are imported,
and using a mapping axiom (which can be generated automatically), we test the target ontology, T1,
against theories in the repository using an automated reasoner. We collect all theories that are
consistent, which constitutes the image of T1 in the
repository. We may repeat this for any number of ontologies. Once we
have all the images, we can construct a notion of similarity and difference.

Similarity in this context, is simply the intersection of
all the target ontologies, yielding the theories which are commonly
consistent to all. Thus, if the Im(T1) = {A, B, C} and Im(T2) = {A, D} and Im(T3) = {A, B, E}, their similarity is Sim(Group)=A.

Difference is slightly more nuanced.
It requires that we pick a single ontology and compare it to a group.
The difference for (T1, Group) are the theories which are consistent
with T1 but inconsistent with at least one Ti in Group. So if Group = {T1,T2,T3}, then Diff(T1,Group) = {B,C}

Next Steps

Michael Gruninger's
Semantic Technologies Laboratory will be implementing one such
repository, using CLIF over the next few months. Work is also starting to map existing UOs into the
repository to populate the second layer. The algorithms should be
implemented as a web accessible service over the summer.

In terms of the ontology design algorithm -- it's only really scratching the surface. Right now it's providing axioms for one relation at a time (though the specification of other relations and functions fall out as a corollary) . It'll be interesting to extend this to multiple relations simultaneously. Also, creating graphics that are more natural for a subject matter expert's particular domain is an interesting extension of the idea.


// ontolog held up my initial message cuz the attachment was >3Mb, so here is a link if you're interested:
http://www.yousendit.com/download/WnBRN3RaMGtmVFpMWEE9PQ

-- 

Cheers,
Ali Hashemi
MASc (waiting to convocate)
Semantic Technologies Laboratory
University of Toronto


PS (i'm graduating in one month, but don't want to start phd till 2010. if anyone has an interesting project (that pays better than grad student salaries) i'd be very interested and willing to move! :P )

-- 
(•`'·.¸(`'·.¸(•)¸.·'´)¸.·'´•) .,., 
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