Re: [ontolog-forum] Next steps in using ontologies as standards

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

Hello all,

I've read the discussion with interest, and it's very interesting how much overlap there has been with my thesis. Unfortunately, I cannot share this until next week, but it will be made available online.

Onto some specifics:

My thoughts on the subject indicate that foundation ontologies are inadequate. They each capture the biases of what people consider to be foundational concept. It is difficult to identify what is being said. However, I sympathize with Pat C's vision. Though I think an ontology repository is more suitable than simply an FO. 

Using a central repository, you might then pick a subset of theories (modules) for which to construct your ontology.

We're not combining ontologies, we're linking them in useful ways.

So to take Pat H's illustration of the 3D vs 4D accounts, while they are in metaphysical opposition, they share patterns of thought, of logic. There _are_ (useful) similarities, just as there are differences.

Moreover, they share a language, and describe the same phenomena. There are links between the two accounts.

They might not be exactly primitive in the sense that they are the "atoms" from which everything else is built. But they do reuse basic logical concepts. I

The repository architecture I propose in my thesis uses this notion. It is similar to the idea of metaphor -- how is the solar system similar to an atom? We are mapping substructures from one concept to another. Is there something special about these patterns?


[Begin Pat C1]
>   Both of these common cases are consistent with, and can benefit from,
> using a logically consistent set of ontological representations of the
> primitive concepts that can accurately describe the alternatives.
[End Pat C1]

[begin Pat Hayes1]
Plain flat wrong. Provably wrong, in fact, in this case. There is no such set of primitive concepts for these ontologies. (Think about it for a second: the only concepts in most of them were those of  timepoint and time-interval, and in all but the simplest, these are in fact interdefinable, so one can make do with one. What more "primitive" concepts can one reduce this set to?)
[end Pat Hayes1]

I disagree (Pat H).  Both these accounts use orderings.  They share many logical structures. There is indeed an undercurrent that pervades both accounts of time, especially if we consider accounts of time as expressed in say, FOL.


***
[begin Neil]
Pat, you said "Again, you seem here to be talking about a comparative meta-theory of alternative ontologies, a kind of uber-meta-ontology which talks about ontologies rather than about the world that those ontologies describe. This is an interesting-sounding idea, but I have no idea how to begin approaching it."

This sounds like the issue The Open Group solved with its Model Driven Architecture with XMI, a meta-meta-data specification for importing and exporting data models from different tools that however all encoded with XML.  What you are discussing is I believe the path to the ontology interoperability solution.  What is needed is exactly what you stated, a framework that will allow both machine and ontologist to tell at what levels two ontologies are ambiguous and at what nodes they become disambiguous. 

This sounds to me to be analagous to determining at what level two people are in complete agreement on an idea and at what point they agree to disagree, marking those points distinctly so that others can discern to which they want to subscribe.

I would say that perhaps even a rating system could be devised based on this idea that could tell the level of congruence between two ontologies and give the user an idea of the continuity based on this rating-- which could even be something as simple to use as a percentage at each node of the ontology.
[end Neil]

The functionality Neil describes here is almost exactly what the semantic mapping algorithm chapter of my thesis elaborates.

I would like to iterate here that what we may often de-emphasize, is that we're capturing _parts of reality_ through languages.

when pat states:

[begin Pat Hayes2]
But my point is that there is only one entity, in fact. And it is important for an ontology to be able to say this, and clearly draw appropriate conclusions. If I am in a room and nobody else is in it, there is one person in the room. Not two people, one of them 4-d and one of them 3-d. 
[end Pat Hayes2]

There is surely only one of Pat, but language affords (at least) two ways of describing him; of creating a coherent account of him. 

We would do well to heed some insights from Marshall McLuhan. "The medium is the message." An ontology is the interplay of a number of media, not least of which is language - generally some formal logic. Ontologies rendered thusly reflect the expressivity and theories of the language.

Possibly a mundane point, but they should also highlight the ways in which inconsistent theories may share similar structures. Indeed, if one were to construct a _model_ (in the logical sense), of pat using 3-d and 4-d views, there would be much in common between the two.

 The interesting question is how they relate. Not that a merge would simply render the resultant account incoherent. But in what ways are they similar and how to they differ?

****
[begin John S]
There are many good resources available on the WWW, but I am not aware of anything that comes close to meeting the above criteria for maintaining, evaluating, relating, and organizing an open-ended
and growing collection of ontologies.  If anyone knows of any such things, please let us know.
[end John S]

one should be forthcoming.
***


[being Ed b]
 If I were more conversant with the Cyc ontology, I probably would have known which collector I wanted in each case, but that is after my domain analysis tells me what axioms I need.  Now, once
I had determined what I meant, I found a Cyc concept had all the needed axioms, including ones I would have forgotten.  OTOH, I had to reject two similar concepts because they included axioms I didn't mean. Without Cyc, I defined (most of) the same general concepts, but it took me several tries to get all the axioms right.
[end Ed b]

how serendipitous, my ontology design algorithm (chapter) partially addresses, and at the very least alleviates a lot of the problems here. it allows ontology designers to define a relation semantically, with little need to navigate the syntax and grammar of a particular formal logic.

***

[begin P hayes3 ]They are all "atomic". (Well, virtually all: all the 'natural kind' concepts, as opposed to artificial combinations such  as "French women between the ages of 25 and 50".) Just look at a first-order theory: all the names in it are on an equal footing; none are more 'primitive' than another, and they have no internal conceptual structure which would permit their being decomposed into something simpler or more elemental.
...
But surely the time catalog is a clear case of this non-uniqueness. I fail to understand how you cannot see this, it seems so obvious. What would you reduce all of it to?
[end P hayes3]

I would reduce it to theories it is reusing. In the case of time, orderings. In the case of space, orderings, groups, symmetries etc. 

There are more links than simply conservative and non-conservative extensions. More than simply generalization and specialization.

Briefly, the repository architecture i've outlined in my thesis consists of two main components:

"Abstraction Layers" -- abstraction layers are connected with one another via representation theorems.
and
"Core Hierarchies" -- no core hierarchy may share a non-conservative extension with another in the same abstraction layer.

It shares some similarities withe the lattice of theories that John Sowa has spoken of, but it has other properties which enable the above two mentioned algorithms.

The repository isn't necessarily an account of the world. It's an account of what's expressible in a formal logic (in the case of my implementation, Common Logic). It is silent as to the disagreements of the Upper Ontologists. It is more interested in finding useful patterns as expressible in language, and only then, how these patterns are related to grounded concepts. 

This idea isn't an attack on UO's, but rather a complement. The different views, and biases as captured by UO's are valuable. It's simply that they are not exclusively "true". The repository described in my thesis unifies these within the language of _expression_.

It also consequently enables to pretty useful algorithms. One for semantic mapping and another for ontology design.
The semantic mapping algorithm uses a centralized repository to conduct ontology alignment between n or more ontologies.
The ontology design algorithm intelligently navigates the repository to match an agent's intended semantics to sets of axioms.

Sorry for the tease, but next week my thesis will be bound and in the libraries, so i'll be able to link the document then.

(PS if someone has an interesting project, i'd likely be interested now that my Master's is complete ;) .)

Ali Hashemi
MASc (waiting to officially convocate)
Semantic Technologies Laboratory
University of Toronto
-- 
(•`'·.¸(`'·.¸(•)¸.·'´)¸.·'´•) .,., 
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