Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping

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

Dear Rob, Sean and John.


On Fri, Mar 12, 2010 at 8:30 AM, Ron 
Wheeler <rwheeler@xxxxxxxxxxxxxxxxxxxxx> 
wrote:

[RW]Are these ideas sufficiently well-formed that we could start to talk
about the metadata required to support the lattice?

<snip>
 

> [RW] Does this imply that a reasoning engine can read the 
> metadata from both
> theories and automatically map data from one to another to actually
> implement the sharing process?

Storing relations between ontologies at a metalevel are approaching the point where we can automatically combine them in many scenarios. 

One such example can be found here:
 http://stl.mie.utoronto.ca/colore/index.html

Please note that the above site is in ... pre-alpha mode. It's purpose right now is simply to illustrate some very basic concepts.

The list displayed at the above URL corresponds to families of ontologies in COLORE. Each of those families of ontologies is a partial ordering of modules (set of axioms), with one or more root modules, with other modules which extend / specialize those roots. In a way, each family corresponds to a snippet of the infinite lattice.

If you click on of those links, say Mereotopologies, you will see a listing of all the Mereotopology Modules contained within that family (or core hierarchy).

At this point in time, the page only displays the metadata connections between ontologies, but let's say we click on Region Connection Calculus ( http://stl.mie.utoronto.ca/colore/mt/RCC.xml )

Here we see the metadata displayed for this ontology (i's axioms are currently not displayed on the page). There are 3 categories of links,

1. Direct Relations (connecting ontologies / modules)
2. Lexicon (if any new terms / relations are introduced in this module)
   
3. Inherited Lexicon (if this module uses terms defined in a "parent" module).

For the purposes of this example, we are only interested in Direct Relations. In the list of Direct Relations between ontologies, we see that RCC is Definably Equivalent with ca:RegionBooleanContactAlgebra, an ontology located in the Contact Algebra hierarchy, where the mapping is defined in the mt:RCC-RBCA module located in the Mereotopology core hierarchy.

With these mappings available, we can easily imagine a service which would read this metadata, determine that RCC is definably equivalent to RBCA, and that the mapping axioms to combine these two theories can be found in mt:RCC-RBCA. Thus, if we want to exchange messages between these two ontologies, or combine them or whatever, we now know what to do.

Additionally, in this case, the mapping is bidirectional and transitive, so any other ontology that is later added to one has an automatic mapping to the other. The definitions of the other types of mappings may be found in this paper:

Gruninger, M., Hashemi, A., and  Ong, D. Ontology 
Verification with Repositories,
to appear in Formal Ontologies and Information Systems 2010.

( http://stl.mie.utoronto.ca/publications/colore-fois.pdf )

Though there are a number of other ontology relations that don't appear in the above paper. However, I think it becomes relatively clear how one can build services on top of this style of metadata capture which enables what you are asking, right?

There are a couple of other tools which enable one to generate axioms based on such a repository by merely exchanging instance level data (i.e. ontology generation by example), and another which enables determining how and where two or more ontologies agree and disagree on terms. A very brief description of this first tool is viewable here: Hashemi, A. and Gruninger, M. (2009) Ontology
 Design Through Modular  Repositories,
 International Conference on Knowledge Engineering and Ontology 
Development.  ( http://stl.mie.utoronto.ca/publications/design-repository.pdf )  

Very briefly as well, the semantic mapping procedure works by taking a proposed mapping (say "Kermit4D = Kermit3D ?") and finding the strongest module in the repository which is consistent with both accounts. It uses readily available theorem provers and consistency checkers. It applies to other types of mappings as well (i.e. is my Cut the same as your Snip ) etc, covering most of the cases Sean outlined above. 

Note: Strongest is defined - If each family of ontologies is a partial ordering, then a module that is an extension of another (i.e. child or specialization) is stronger by virtue of the fact that more theorems may be proven (i.e. it says more).

In any event, I imagine the OOR usecase session and forthcoming COLORE usecase scenarios will shed more light on how to leverage such an architecture and ensuing services for several types of interoperability / ontology design problems.

Cheers,

Ali



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