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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 16 Jan 2009 16:29:47 -0600
Message-id: <659C1D73-1EF2-4213-ADC7-8B745D3F2B2A@xxxxxxx>

On Jan 16, 2009, at 11:01 AM, Ali Hashemi wrote:

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.

Well, that sounds nice, but until you clarify what you mean, its impossible to evaluate it. What does it mean to link as opposed to combine ontologies? I take it that 'combine' means simply to take two sets of axioms and make them into one set. This is the (admittedly very basic and elementary) sense implied by the OWL 'import' primitive, where one ontology can 'combine another ontology into itself. I have never seen any more nuanced or subtle form of combination or 'linking' ever precisely defined. 

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.

There are indeed similarities. They are so similar in fact that it is hard for many people to even perceive the differences between them. Intuitively they are indistinguishable. But therein lies the problem: because our reasoning engines have no intuition, and formally they (the theories) are incompatible. Intuitive similarity means very little when it comes to ontologies. An analogy: consider two cars made by different manufacturers. They both have similar overall structure, similar shapes and very similar performance and behavior in the real world. But it would be a grave mistake to assume from this that they had interchangeable parts. 

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

In a survey talk a few years ago, I introduced the notion of the 'diamond of confusion'. Take two intelligent, competent people who both know logic, and tell them to use identically the same formalism (the bottom of the diamond) and to formalize the same sets of intuitive concepts, such as time and change and identity (the top of the diamond). They will not produce the same ontologies. There is every likelihood, based on actual experience so far, that they will produce logically incompatible ontologies (the two sides of the diamond). Similarity, or even identity, of the topic and of the formalism, is NOT a guarantee that ontologies will be in any useful way formally similar or even formally compatible. 

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. 

But not the same metaphysical concepts. Continuants are simply impossible in a strict 4-d ontology, for example. 

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?

It would be great, wonderful, if ontologies could make use of metaphor-like relationships. There has been some preliminary work along these lines, based on a notion of metaphoric structural mappings developed at Northwestern University by Ken Forbus and his students. I think it is fair to say that this has not yet reached the ontology mainstream, though John Sowa may have something to say about this.

We are mapping substructures from one concept to another. Is there something special about these patterns?

In what sense of special? (Psychological? Practical? Engineering? Logical? ...?)

[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 all use different notions of order, though. As I said earlier, if you seek what is common to them all, what you get is a very minimal notion, that time-points are partially ordered. That alone is not enough for a useful temporal ontology. 

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.

Of course. But one part of reality might be described in many different, equally valid, ways. 

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.

Sure, of course. But my point was that PatC's suggested strategy of including all these alternatives into one ontology, yields an ontology which says that are two of Pat. This, which might be called the thousand-flower strategy, cannot distinguish between two things and two descriptions of one thing. That was my point. 

We would do well to heed some insights from Marshall McLuhan. "The medium is the message."

Not to put too fine a point on it: bullshit. Or as Korzybsky said, quite a few years before McLuhan: "The map is not the territory". 

(As you can no doubt tell, I have very little respect for McLuhan, either as a person or as an intellectual guide. IMO, his writings are vaporware. He believed he was in direct communion with the Virgin Mary and was obsessed with the number three. But in any case, nothing he wrote has the remotest bearing on ontology engineering.)

An ontology is the interplay of a number of media, not least of which is language - generally some formal logic.

This is nonsense. Logic is not a medium in McLuhan's sense, because it is not a language in his sense. Formal logics are not (yet) media for human or societal communication. 

Ontologies rendered thusly reflect the expressivity and theories of the language.

First-order logic imposes the following conditions on the worlds it describes:

1. The world contains entities which can be conceptually distinguished from one another, and stand in relations to one another.
2. The world is not empty: it contains at least one entity. 

And that is all it imposes. This is about the weakest set of conditions one could possibly imagine for an ontology language. It would be ridiculous to conclude that the use of FOL as an ontology language was subject to vague McLuhanesque critiques of imposing its own agenda on theories written in it. 

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.

Not sure what you mean by _model_ here. I have to presume you don't mean as in model theory, so I'm guessing you actually mean something like 'logical ontology'.  And they do have a lot in common in some sense, but not in any sense that I know how to make precise. Perhaps you can do better. 

 The interesting question is how they relate.

That has been worked out in some detail in this particular case. 

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.

To my mind, that is saying that you can define it semantically without semantics (since any precise semantics must be attached to a formal grammar of some kind, if only a very 'abstract' one.)


[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.

I suggest that you actually read the catalog before proceeding. There are some re-use cases in there, where one theory extends or builds on another. But there are also a number of clear incompatibilities between different alternative building blocks. To take the first: are times dense or not? Some time-orderings assume a discrete ordering in which each time has a unique 'next' time. These correspond to the time "theories" incorporated into for example the UNIX operating system, where all times and dates are defined as a number of milliseconds since the start of 1970. Other temporal ontologies require time to be continuous, or at least dense. These are incompatible: in fact, one gets an early version of the first by explicitly denying a basic axiom of the second. Others still use other, more complex, order structures. These are not re-uses of one theory: they are different, incompatible, basic theories which have ramifications throughout the subsequent development of more complex theories. For example, some of them make the familiar algebra of 13 interval relations incoherent, others reduce it to fewer relations, and others still allow 16 relations (if time is allowed to be circular). 

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.
"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.

That sounds interesting. Please don't take this the wrong way, but it sounds almost too interesting to be a master's thesis. But I look forward to reading it. 

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.

I look forward to seeing it. Until then, let us all hope you are onto something. I have to say, anyone who can bring together Common Logic and Marshall McLuhan and make something meaningful from this collision will have my respect. :-)


(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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